{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "eec23018",
   "metadata": {},
   "source": [
    "# Discrete Time Sensor Fusion\n",
    "RMM, 24 Feb 2022\n",
    "\n",
    "In this example we work through estimation of the state of a car changing lanes with two different sensors available: one with good longitudinal accuracy and the other with good lateral accuracy.\n",
    "\n",
    "All calculations are done in discrete time, using both a Kalman filter formulation and predictor-corrector form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "107a6613",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import control as ct\n",
    "import control.optimal as opt\n",
    "import control.flatsys as fs\n",
    "\n",
    "# Define line styles\n",
    "ebarstyle = {'elinewidth': 0.5, 'capsize': 2}\n",
    "xdstyle = {'color': 'k', 'linestyle': '--', 'linewidth': 0.5, \n",
    "           'marker': '+', 'markersize': 4}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea8807a4",
   "metadata": {},
   "source": [
    "## System definition\n",
    "\n",
    "We consider a bicycle model for an automobile:\n",
    "\n",
    "<img src=\"../examples/vehicle-steering.png\" width=\"400\"/>\n",
    "\n",
    "### Continuous time model\n",
    "The dynamics are given by\n",
    "\n",
    "$$\n",
    "  \\begin{aligned}\n",
    "    \\dot x &= \\cos\\theta \\, v, \\qquad\n",
    "    \\dot y &= \\sin\\theta \\, v, \\qquad\n",
    "    \\dot \\theta &= \\frac{v}{l} \\tan\\phi,\n",
    "  \\end{aligned}\n",
    "$$\n",
    "\n",
    "where $(x, y, \\theta)$ are the position and orientation of the vehicle, $v$ is the forward velocity, $\\phi$ is the steering wheel angle, and $l$ is the wheelbase.\n",
    "\n",
    "These dynamics are included in the file `vehicle.py`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a04106f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<FlatSystem>: vehicle\n",
      "Inputs (2): ['v', 'delta']\n",
      "Outputs (3): ['x', 'y', 'theta']\n",
      "States (3): ['x', 'y', 'theta']\n",
      "\n",
      "Update: <function _vehicle_update at 0x140a4a2a0>\n",
      "Output: <function _vehicle_output at 0x140a4a340>\n",
      "\n",
      "Forward: <function _vehicle_flat_forward at 0x140a4a160>\n",
      "Reverse: <function _vehicle_flat_reverse at 0x140a4a200>\n"
     ]
    }
   ],
   "source": [
    "# Vehicle steering dynamics\n",
    "#\n",
    "# System state: x, y, theta\n",
    "# System input: v, phi\n",
    "# System output: x, y\n",
    "# System parameters: wheelbase, maxsteer\n",
    "#\n",
    "from vehicle import vehicle, plot_lanechange\n",
    "print(vehicle)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8ae0344",
   "metadata": {},
   "source": [
    "This system is differentially flat and so we can define a trajectory for the system using the `flatsys` module.  We generate a motion that corresponds to changing lanes on a road:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69c048ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
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aLTRaQEBACECrFdCKmudaUfN+WlG7rvb5taNe146DXTssJpVK8MrYkFb9uTTlVC4Gu2YSQmDu3LkYOHAgunbtet12ixYtwoIFC9qwMiIiIv3QagWKK9UoKqtGYXkVisqrUVKhRkmlGmVVmtqvapRWalBaqUbpVd/Xtamorg1vtcHN0I4nytog2DUFg10zPfPMMzh58iT27Nlzw3bz58/H3Llzdc/rhlGJiIjaMyEECsuqkVdSidziSuSWVCKvpAqFZVUoLKtGUXk1CsurUVRWpfteVV4NbSsGMYWJtOZhKoPCRAq5iRRymRQmMglMpFKYSCWQSSUwlUkhk0pgIpXo1tU9l0olkEoAqUQCiaRm9EsqASSo/Vq7XCqRQIKaEbirSa7zRFL7pL1cF8lg1wzPPvssNm7ciF27dt305EWFQgGFQtFGlREREd2YWqNFTnElMgrLkVlUgZziSuSVVCJPF94qkVdchbySSqhvMaWZm8qgNDeF0twU1mYmsFSYwFIhg6X8qu8VJleey2W65eamJlCY1gY4E5nue7lMytkkmoHBrgmEEHj22WexYcMGREdHw8/PT98lERER6Wi1AvmlVcgsKkdGYTkyCitqvi+qQGZtkMtWVTRrVE1pbgpHKzmcrBVwtFLA3lKuC222FvLar6awrV1mY24KM1NZ6+0kNQmDXRM8/fTT+Omnn/Dnn3/C2toaWVlZAAClUglzc3M9V0dERB1BpVqDtMvlSMkvQ3J+KZILymq+LyhDSkEZqtTam27DVCaBq9IMbkpzONcGNidrBZysFHC0luueO1gqIDfhPQwMEac7aYLrDQGvXr0a06ZNa9I2VCoVlEolioqKeFUsERE1qkqtRXJ+KS7mliAprwwpBaVIzi9Dcn4ZMorKb3hBgUQCOFsr4KY0h7utGdyV5nCzNYe70kz31dFK0eDcMWr/mpMhOGLXBMy+RETUksqq1LiYU4oLucU4n12CCzkluJBbguT8MmhucLzUQi6Dt70FfBws4ONgCW97C/g6WMLHwQKuSjOYyjjK1tEx2BEREbWS8ioNErKLEZepqglwuSW4mFOC9MLy677GSmGCTs5W8HOwgLeDJXzsLeDraAFve0s4Wsl5IQHdEIMdERHRbRJCIEtVgbhMFeIyi3E2U4W4TBUu5ZVe94IFB0s5OjlbobOzFQKuerjamDG80S1jsCMiImqGao0W57KLcTajJsTFZaoQl6VCYVl1o+0dreQIcbNBZ2drBDhbobOLFQKcrGBnKW/jyqkjYLAjIiK6Do1WIDG3BCfTinAyrRAn0opwNlPV6BWoMqkEnZwsEeJmc9XDGs7WZnqonDoqBjsiIiLUHE5NLSjHibRCnEwrxMm0IpxOL0JplaZBWxszE4S6XwlwoW42CHC24jxupHcMdkRE1CEVV1TjeGohjiZfxrGUmjDX2OFUc1MZunko0c1TiTBPJbp72sLHwYLnwVG7xGBHRERGTwiBlIIyHE2+rHskZBc3mBdOLpMixM0aYZ626FYb4gKcrSDj3G9kIBjsiIjI6FRUa3AqvahmNC75Mo6lXEZeSVWDdl725gj3tkMvHzv08LJFkKs1FCY8nEqGi8GOiIgMXmmlGkeTL+NgUj4OJhbgRFohqjX1h+PkMim6eSoR7mOHXt526OVjywsbyOgw2BERkcEpKq/G0eQCHEwswIGkApxOL2pwxwZHKwV6+9jVBDkfO3T1sOFoHBk9BjsiImr3LpdW4dClmiB3MCkfZzNVDc6P87A1R4S/Pfr6OaCPnz0vcKAOicGOiIjandJKNQ4lFWDvhTzsvZiPuExVgza+DhaI8HNAhL89+vjZw9POQg+VErUvDHZERKR3VWotjqcWYu+FPOy7mIfYlEKorzm0GuBshQg/e0T4OyDCzx4uNjw/juhaDHZERNTmtFqBs5kq7LuYh70X8nEoqQDl1fUnAva0M8eATo7oH+CA/p0c4WSt0FO1RIaDwY6IiNpEZlE5dp/Lw67zudh7IQ+Xr5kM2MFSjn6dHDAgwBEDOjnC24GHVomai8GOiIhaRUW1BgeTCrDrXC52n8/FueySeust5TJE+Dugf22YC3KxhpQTARPdFgY7IiJqEUIInMsuwa5zudh1PhcHkwpQpdbq1kskQHdPWwzu7IjBgU7o7mULU5lUjxUTGZ92H+zs7e2b1V4ikeDYsWPw8fFppYqIiKhOUXk1dp/PRXRCzahctqqy3no3pRkGd3bCoEBHDAxwhK2FXE+VEnUM7T7YFRYWYtmyZVAqlTdtK4TA7NmzodFobtqWiIiaTwiBuMxiRJ/LQXR8Lo6mXK43MbDCRIq+/g4Y1NkRQwKdEOBsxbnkiNpQuw92APDggw/C2dm5SW2fffbZVq6GiKhjKa6oxt4L+YhOyEF0Qi6yVBX11gc4W2FooBOGBDnhDl97mJny7g5E+tLug51Wq715o6sUFxe3UiVERB2DEAIXckqwMyEHO+NzcfhSQb055cxMpRjQyRFDg50xNNAJXva8epWovWj3wY6IiFpf3RWsO+KysT0+B2mXy+ut93O0xNAgJwwNckaEH0fliNorgwt26enp2Lt3L3JychqM5j333HN6qoqIyPDkqCqwMyEH2+NysOdCHsqqrpyfLDeRop+/gy7M+Tla6rFSImoqgwp2q1evxqxZsyCXy+Hg4FDvhFyJRMJgR0R0A1qtwJkMFbbHZ2NHfA5OphXVW+9srcCIEGcMD3bBgAAHWMgN6k8EEQGQCCHEzZu1D15eXpg1axbmz58PqdSw5j5SqVRQKpUoKiqCjY2Nvsshog6ivEqDPRfysD2uJszlFNefjqS7pxLDg10wIsQZXdxteAUrUTvUnAxhUB/HysrK8OCDDxpcqCMiaks5qgpsj8/BtrPZ2HMhD5VXTRJsIZdhUGdHjAh2wdBgJzhbm+mxUiJqaQYV7GbMmIHffvsNL7/8sr5LISJqN+rmltsWl43tcdk4cc0hVg9bc9wZ4owRIS6I8LeHwoQXPhAZK4M6FKvRaDB+/HiUl5ejW7duMDU1rbf+ww8/1FNlN8dDsUTUkirVGhxMLKgNczlIL6x/FWsPL1vcGeKMO0NdEORizUOsRAbMaA/FLly4EP/++y+CgoIAoMHFE0RExqywrAo7E3IQdTYbu87loaRSrVtnZirFwAAnjAx1xrBgZx5iJeqgDCrYffjhh/jmm28wbdo0vbz/8uXL8d577yEzMxNdunTBsmXLMGjQIL3UQkQdQ3J+KaLOZmNbXDYOX6p/+66aq1hdcGeIMwYEOHJuOSIyrGCnUCgwYMAAvbz32rVrMWfOHCxfvhwDBgzAypUrMWbMGJw9exbe3t56qYmIjI9WK3A8rRDbasPcueySeuuDXa0xMtQFI0JcEOahhFTKoxVEdIVBnWO3aNEiZGZm4pNPPmnz946IiECvXr2wYsUK3bKQkBBMmjQJixYtuunreY4dEV1PRbUGey/k1Y7M5SCv5MqUJDKpBBF+9hgZ6oI7Q1x4+y6iDshoz7E7dOgQduzYgb/++gtdunRpcPHE+vXrW+V9q6qqcPTo0QZX40ZGRmLfvn2NvqayshKVlVd+OatUqlapjYgMU15JJXbE15wvt/t8Liqqr0xJYq0wwZAgJ4wMdcHQQGcoLUxvsCUioisMKtjZ2trinnvuafP3zcvLg0ajgYuLS73lLi4uyMrKavQ1ixYtwoIFC9qiPCIyAEIIXMwtxba4bESdzcaxlMu4+niJu9KsZlQu1AURfg6Qm3C+TiJqPoMKdqtXr9br+1975a0Q4rpX486fPx9z587VPVepVPDy8mrV+oiofdFoBY4mX9aFuaS80nrru3rYYGSIK+4MdUaoG+/6QES3z6CCnb44OjpCJpM1GJ3LyclpMIpXR6FQQKFQtEV5RNSOlFaqsft8LqLO5mBHfDYul1Xr1sllUvTr5IA7Q2uuZHVTmuuxUiIyRu0+2PXq1Qvbt2+HnZ1dk9oPHDgQa9euhYeHR4vVIJfLER4ejqioKNx999265VFRUZg4cWKLvQ8RGaaMwnJsj6u58GH/xXxUaa6cL2drYYrhQTUTBQ/q7AhrM54vR0Stp90Hu+PHj+PEiROwt7dvcvurL1poKXPnzsWUKVPQu3dv9OvXD6tWrUJKSgpmzZrV4u9FRO2bEAKn01WIqr2F15mM+hdH+ThY4M4QF4wMdUFvHzuYyHi+HBG1jXYf7ABgxIgRaOqsLK11jsrkyZORn5+Pt956C5mZmejatSv++ecf+Pj4tMr7EVH7UlGtwb6LedgWl4PtcdnIVl35ACmRAOHedrpDrJ2crHi+HBHpRbufxy45ObnZr/H09IRM1r5mYOc8dkSGJ1tVgZ3xOdgen4M95/NQXq3RrbOQyzC4sxPuDHXBsCAnOFjxnFoiah1GNY8dR8SIqK1otQKnM4qwPS4HO+JzcCq9qN56N6UZRoQ4484QF/T1d+AtvIio3Wn3wY6IqDWVVqqx50IedsTlYEdCDnKL6x9i7e5pi+HBzhge7Iwu7pyShIjaNwY7IupwUgvKsKP2EOuBa65itZTLMDjQCcODnTE0yBlO1jzESkSGg8GOiIxepVqDw0mXsTMhB9EJObiYW3+iYG97C4wIccaIYBfc4WcHhQkPsRKRYWKwIyKjlF5YjuiEHEQn5GLvhTyUVV258MFEKkG4jx1GhDhjeLALOjlZ8hArERkFgwp206ZNw/Tp0zF48GB9l0JE7Uy1Rosjly4j+lwOouNzkZBdXG+9k7UCw4KcMCzIGQM6O8KGEwUTkREyqGBXXFyMyMhIeHl54fHHH8fUqVNb9A4TRGRYUgvKsOt8Lnady8W+C/korlTr1kklQC9vOwwLdsaQQCde+EBEHUK7n8fuWvn5+fjhhx+wZs0anD59GnfeeSdmzJiBiRMnwtS0/X4C5zx2RLevtFKN/Rfzsft8Lnadz0NSXv1z5Rws5RgS6IShwc4Y3NkRthZyPVVKRNRympMhDC7YXS02NhbffPMNvvrqK1hZWeHRRx/F7Nmz0blzZ32X1gCDHVHzabUCZzNViDmXi93nc3E0+TKqNVd+ZcmkEvTytsXgzk4YHOiEbh5KSKUclSMi42JUExRfT2ZmJrZu3YqtW7dCJpNh7NixOHPmDEJDQ7F06VK88MIL+i6RiG5BRmE59l7Iw54LedhzPg/5pVX11nvbW2BwoCMGdXZC/04OsOa5ckREOgYV7Kqrq7Fx40asXr0aW7duRVhYGF544QU88sgjsLa2BgD88ssveOqppxjsiAxEYVkV9l/Mx54Ledh3Mb/B4VVLuQz9OjliSG2Y83W01FOlRETtn0EFOzc3N2i1Wjz00EM4dOgQevTo0aDNqFGjYGtr2+a1EVHTlFWpcfjSZey7kIe9F/NwJkOFq08IkUqAME9bDAhwwKDOTujlbQe5iVR/BRMRGRCDCnYfffQR7r//fpiZmV23jZ2dHZKSktqwKiK6kUq1BidSi7D/Yj72XsxDbEr98+QAoLOzFQYEOGJAgCMi/O05FQkR0S0yqGA3ZcoUfZdARDdRXqVBbMplHEgqwKGkfMSmFKJSra3XxsPWHP07OWBAgCP6d3KAs831P6wREVHTGVSwI6L2p6RSjaPJl3EwMR8HkwpwMq2wwYico5UcEX4O6B/ggAGdHOHjYME55YiIWgGDHRE1S35JJY6lFOLwpQIcTMzH6QwVNNr6Qc7VxgwR/vbo42ePCD8H3rKLiKiNMNgR0XVptQLnc0pwNPkyjiZfxrGUyw2uWgUATztz9PGzR18/B0T428PbniNyRET6wGBHRDrFFdU4nlqoC3LHUwrr3aarToCzFcK97RDhb48Ifwd42JrroVoiIroWgx1RB1Wt0eJcdjFOphXhZFoRYlMuIyG7GNfei8ZCLkMPL1uE+9ihl48denrZ8lZdRETtFIMdUQeg1Qok5pXiZFohTqYV4URaIc5mqBpcrQrUHFYN97GrCXLedgh2tYaJjPPIEREZAgY7IiOj1QqkXi7D6XQVTqYV4kRaIU6nq1DSyCFVa4UJunkqEeZpi+6eSvTysYMLpx4hIjJYDHZEBqysSo34rGLEZapqH8WIz1ShtErToK2ZqRRd3ZXo5qlEd09bhHkq4etgCamUFzkQERkLBjsiAyCEQEZRBeIyagNcVk2Iu5Rf2uCcOACQm0gR7GqNbh61Ic5LiQAnKx5SJSIycgx2RO2IRiuQdrkMF3JKcD6nBBdqHxdzShq9OhUAnKwVCHGzQYibNULdbBDqZgM/R0uGOCKiDojBjkgPKqo1SM4vw/mcYl14u5BTgsS8UlQ1ckEDAJhIJQhwttKFuJqvNnC0UrRx9URE1F4x2BG1kqLyaqTklyG5oBTJ+WVIyS/DpfxSpBSUIUtV0eghVKDmMGonJysEOFshoPZrZxcr+DhYQGEia9udICIig8JgR3SLyqrUyCisQGZROTIKy5F2uRzJ+WVILihDcn4pCsuqb/h6a4UJOjnXBrfarwHOVvC0s4CMFzQQEdEtYLAjakSlWoPsokpkFJXXBrcK3deMwnJkFlWgqPzGwQ0AHK0U8HGwgI+9BbwdLODjYAFve0v4OFjAwVLO224REVGLYrC7iUuXLuHtt9/Gjh07kJWVBXd3dzz66KN49dVXIZdz9n1DUqnWIK+kCnnFlcgrqURu7de8kirkFlcit+TK8uKKxi9UuJa1wgRutmZwU5rDw84cPvZXwpu3gwWsFPwvRkREbYd/dW4iPj4eWq0WK1euREBAAE6fPo2ZM2eitLQU77//vr7L63Aq1RqUVWpQUqlGcYUaheVVUJVXo7CsGoXl1Siq/b6ovEr3fWFZNVTl1de9qvR65CZSuCtrQpu7rTncawOcm60Z3Gu/2piZttKeEhERNZ9EiOudwk3X895772HFihVITExs8mtUKhWUSiWKiopgY2PTitW1LiEE1FoBjVagWqOFRlvzXK0RUGu1tcuvrK+o1qBSrUWlWoPKau2V79Xa2ud167Uoq1KjtFKD0ko1Sq/6vqyqJsiVValRrbm9f66mMgkcrRRwslbA0UoBRyt57dcry5ysa5YpzU15qJSIiPSuORmCI3a3oKioCPb29jdsU1lZicrKSt1zlUrVavWcySjCzG+P1Ft2bfy5Nr4LCAhR004IAa0AtKJm2fW+akRNYGsPzEylsFKYwtbCFLbmNV9tzE1hay6HrYUplLXLlOZ138thbyGHjbkJwxoRERktBrtmunjxIj799FN88MEHN2y3aNEiLFiwoE1qqtbU3JVAn0ykEsikEpjKpJBJJTCRSiA3kUJhIoXCRAaF6VXfm0hrn9d8b2Yqg9xECnNTGSwVMlgqTGApN6n9Wvu8drmFvGYZJ98lIiJqqMMein3zzTdvGrwOHz6M3r17655nZGRgyJAhGDJkCL766qsbvraxETsvL69WORRbVqXGxZzSBstvNjAlkQBSiQRSiaT2e0AikUCC+ssltct14U0qhUxW87xuGUfBiIiIWkdzDsV22GCXl5eHvLy8G7bx9fWFmZkZgJpQN2zYMERERGDNmjWQSps3YmQs59gRERFR2+I5dk3g6OgIR0fHJrVNT0/HsGHDEB4ejtWrVzc71AE157EBrXuuHRERERmfuuzQlLG4DhvsmiojIwNDhw6Ft7c33n//feTm5urWubq6Nnk7xcXFAAAvL68Wr5GIiIiMX3FxMZRK5Q3bdNhDsU21Zs0aPP74442ua86PTqvVIiMjA9bW1q1yPlrdOXypqakd4lAv99e4cX+NX0fbZ+6vcWvt/RVCoLi4GO7u7jc9asgRu5uYNm0apk2bdtvbkUql8PT0vP2CbsLGxqZD/Ceqw/01btxf49fR9pn7a9xac39vNlJXh3NGEBERERkJBjsiIiIiI8FgZyQUCgXeeOMNKBQKfZfSJri/xo37a/w62j5zf41be9pfXjxBREREZCQ4YkdERERkJBjsiIiIiIwEgx0RERGRkWCwIyIiIjISDHZGYPny5fDz84OZmRnCw8Oxe/dufZfUat58801IJJJ6j+bc2q2927VrF+666y64u7tDIpHgjz/+qLdeCIE333wT7u7uMDc3x9ChQ3HmzBn9FNsCbra/06ZNa9Dfffv21U+xLWDRokW44447YG1tDWdnZ0yaNAkJCQn12hhTHzdlf42pj1esWIGwsDDdJLX9+vXD5s2bdeuNqW+Bm++vMfVtYxYtWgSJRII5c+bolrWHPmawM3Br167FnDlz8OqrryI2NhaDBg3CmDFjkJKSou/SWk2XLl2QmZmpe5w6dUrfJbWY0tJSdO/eHZ999lmj65cuXYoPP/wQn332GQ4fPgxXV1eMHDlSdy9iQ3Oz/QWA0aNH1+vvf/75pw0rbFkxMTF4+umnceDAAURFRUGtViMyMhKlpaW6NsbUx03ZX8B4+tjT0xOLFy/GkSNHcOTIEQwfPhwTJ07U/WE3pr4Fbr6/gPH07bUOHz6MVatWISwsrN7ydtHHggxanz59xKxZs+otCw4OFi+//LKeKmpdb7zxhujevbu+y2gTAMSGDRt0z7VarXB1dRWLFy/WLauoqBBKpVJ88cUXeqiwZV27v0IIMXXqVDFx4kS91NMWcnJyBAARExMjhDD+Pr52f4Uw/j62s7MTX331ldH3bZ26/RXCePu2uLhYdO7cWURFRYkhQ4aI559/XgjRfv7/csTOgFVVVeHo0aOIjIystzwyMhL79u3TU1Wt7/z583B3d4efnx8efPBBJCYm6rukNpGUlISsrKx6/a1QKDBkyBCj7u/o6Gg4OzsjMDAQM2fORE5Ojr5LajFFRUUAAHt7ewDG38fX7m8dY+xjjUaDX375BaWlpejXr5/R9+21+1vHGPv26aefxrhx43DnnXfWW95e+tikzd6JWlxeXh40Gg1cXFzqLXdxcUFWVpaeqmpdERER+O677xAYGIjs7Gy888476N+/P86cOQMHBwd9l9eq6vq0sf5OTk7WR0mtbsyYMbj//vvh4+ODpKQkvPbaaxg+fDiOHj3aLmZ4vx1CCMydOxcDBw5E165dARh3Hze2v4Dx9fGpU6fQr18/VFRUwMrKChs2bEBoaKjuD7ux9e319hcwvr4FgF9++QXHjh3D4cOHG6xrL/9/GeyMgEQiqfdcCNFgmbEYM2aM7vtu3bqhX79+6NSpE7799lvMnTtXj5W1nY7U35MnT9Z937VrV/Tu3Rs+Pj74+++/cc899+ixstv3zDPP4OTJk9izZ0+DdcbYx9fbX2Pr46CgIBw/fhyFhYVYt24dpk6dipiYGN16Y+vb6+1vaGio0fVtamoqnn/+eWzduhVmZmbXbafvPuahWAPm6OgImUzWYHQuJyenwScGY2VpaYlu3brh/Pnz+i6l1dVd/duR+9vNzQ0+Pj4G39/PPvssNm7ciJ07d8LT01O33Fj7+Hr72xhD72O5XI6AgAD07t0bixYtQvfu3fHxxx8bbd9eb38bY+h9e/ToUeTk5CA8PBwmJiYwMTFBTEwMPvnkE5iYmOj6Ud99zGBnwORyOcLDwxEVFVVveVRUFPr376+nqtpWZWUl4uLi4Obmpu9SWp2fnx9cXV3r9XdVVRViYmI6TH/n5+cjNTXVYPtbCIFnnnkG69evx44dO+Dn51dvvbH18c32tzGG3sfXEkKgsrLS6Pr2eur2tzGG3rcjRozAqVOncPz4cd2jd+/eeOSRR3D8+HH4+/u3jz5us8s0qFX88ssvwtTUVHz99dfi7NmzYs6cOcLS0lJcunRJ36W1innz5ono6GiRmJgoDhw4IMaPHy+sra2NZn+Li4tFbGysiI2NFQDEhx9+KGJjY0VycrIQQojFixcLpVIp1q9fL06dOiUeeugh4ebmJlQqlZ4rvzU32t/i4mIxb948sW/fPpGUlCR27twp+vXrJzw8PAx2f5966imhVCpFdHS0yMzM1D3Kysp0bYypj2+2v8bWx/Pnzxe7du0SSUlJ4uTJk+KVV14RUqlUbN26VQhhXH0rxI3319j69nquvipWiPbRxwx2RuDzzz8XPj4+Qi6Xi169etWbSsDYTJ48Wbi5uQlTU1Ph7u4u7rnnHnHmzBl9l9Vidu7cKQA0eEydOlUIUXM5/RtvvCFcXV2FQqEQgwcPFqdOndJv0bfhRvtbVlYmIiMjhZOTkzA1NRXe3t5i6tSpIiUlRd9l37LG9hWAWL16ta6NMfXxzfbX2Pp4+vTput/FTk5OYsSIEbpQJ4Rx9a0QN95fY+vb67k22LWHPpYIIUTbjQ8SERERUWvhOXZERERERoLBjoiIiMhIMNgRERERGQkGOyIiIiIjwWBHREREZCQY7IiIiIiMBIMdERERkZFgsCMiIiIyEgx2RERt7NKlS5BIJJBIJOjRo8dtb69uW7a2tre9LSIybAx2RER6sm3bNmzfvv22t5OZmYlly5bdfkFEZPAY7IiI9MTBwQEODg63vR1XV1colcoWqIiIDB2DHRHRbcjNzYWrqysWLlyoW3bw4EHI5XJs3bq1WduaNm0aJk2ahIULF8LFxQW2trZYsGAB1Go1/ve//8He3h6enp745ptvWno3iMhImOi7ACIiQ+bk5IRvvvkGkyZNQmRkJIKDg/Hoo49i9uzZiIyMbPb2duzYAU9PT+zatQt79+7FjBkzsH//fgwePBgHDx7E2rVrMWvWLIwcORJeXl6tsEdEZMg4YkdEdJvGjh2LmTNn4pFHHsGsWbNgZmaGxYsX39K27O3t8cknnyAoKAjTp09HUFAQysrK8Morr6Bz586YP38+5HI59u7d28J7QUTGgMGOiKgFvP/++1Cr1fj111/x448/wszM7Ja206VLF0ilV341u7i4oFu3brrnMpkMDg4OyMnJue2aicj4MNgREbWAxMREZGRkQKvVIjk5+Za3Y2pqWu+5RCJpdJlWq73l9yAi48Vz7IiIblNVVRUeeeQRTJ48GcHBwZgxYwZOnToFFxcXfZdGRB0MR+yIiG7Tq6++iqKiInzyySd48cUXERISghkzZui7LCLqgBjsiIhuQ3R0NJYtW4bvv/8eNjY2kEql+P7777Fnzx6sWLFC3+URUQfDQ7FERLdh6NChqK6urrfM29sbhYWFzd7WmjVrGiyLjo5usOzSpUvN3jYRdQwMdkREetK/f3/06NED+/btu63tWFlZQa1W3/KVuERkPBjsiIjamKenJ86fPw8AUCgUt72948ePA6iZCoWIOjaJEELouwgiIiIiun28eIKIiIjISDDYERERERkJBjsiIiIiI8FgR0RERGQkGOyIiIiIjASDHREREZGRYLAjIiIiMhIMdkRERERGgsGOiIiIyEgw2BEREREZCQY7IiIiIiPBYEdERERkJEz08aa9evVqVnuJRIKNGzfCw8OjlSpqfVqtFhkZGbC2toZEItF3OURERGQghBAoLi6Gu7s7pNIbj8npJdgdP34c8+bNg5WV1U3bCiGwePFiVFZWtkFlrScjIwNeXl76LoOIiIgMVGpqKjw9PW/YRiKEEG1Uj45UKkVWVhacnZ2b1N7a2honTpyAv79/K1fWeoqKimBra4vU1FTY2NjouxwiIiIyECqVCl5eXigsLIRSqbxhW72M2CUlJcHJyanJ7c+ePQt3d/dWrKj11R1+tbGxYbAjIiKiZmvKqVx6CXY+Pj7Nas9DmERkaIQQqKjWQlVRjaLyaqjKa79WVKOorBpF5ep668qrNbBSmEBpbgqluSls6h5mJrrnSnNT2JjVfJWb8No3ImpIL8Hualu2bIGVlRUGDhwIAPj888/x5ZdfIjQ0FJ9//jns7Oz0XCER0Y2pKqpxNkOFMxkqnMkowtkMFRLzSlGl1rbae1opTNDZxQpd3G3QxV2JLu42CHSxhpmprNXek4jaP72cY3e1bt26YcmSJRg7dixOnTqFO+64A3PnzsWOHTsQEhKC1atX67O8FqNSqaBUKlFUVMRDsUQGSgiBnOLK2hBXVBvkVEgpKLvua2RSCWzMTBqMuNmYm9SOyNU8NzOVobRSrRvBuzKap74y0ldejeIK9XXfy0QqQYCzFUKvCnuh7jawMTNtjR8HEbWR5mQIvY/YJSUlITQ0FACwbt06jB8/HgsXLsSxY8cwduxYPVdHRB1dUl4pos5mYe+FfJzJKEJeSVWj7TxszWsDlQ1C3WwQ7GoDeys5LOWyFp3iSKMVKKlQI6e4AmczVfVGCi+XVSM+qxjxWcVYfyxd9xove3N081BiSKATRoS4wNFK0WL1EFH7ovdgJ5fLUVZW82l327ZteOyxxwAA9vb2UKlU+iyNiDogrVbgeFohos5mI+psNi7klNRbL5UA/k51h0BrRsZC3WxgZylvk/pkUgmUFqZQWpiis4s1Jvaomd9TCIHMogpdyDuTURP60gvLkVpQ8/jnVBYkklPo5W2HkaEuGBnqgk5ON592iogMh94PxU6YMAFVVVUYMGAA3n77bSQlJcHDwwNbt27FM888g3PnzumzvBbDQ7FE7VdFtQb7LuYh6mw2tsXlILf4yryZJlIJ+vo7YHiwM3p42yLY1RoWcr1/Jm6yy6VVOJupwpFLlxEVl4XT6fU/MHdyssTIUFeMDHVBTy9bSKWcQJ2ovWlOhtB7sEtJScHs2bORmpqK5557DjNmzAAAvPDCC9BoNPjkk0/0WV6LYbAjal8ul1ZhR3wOos5mY9f5XJRVaXTrrBUmGBLkhJGhLhga5AylufGco5ZRWI5tcTWjkfsv5kOtvfInwNFKgTtDnDEy1AUDAhx5IQZRO2EQwW7r1q0YNmwYTE2N5xfmjTDYEemfRiuw61wuvj+QjJhzudBcFWpcbcx0hyf7+jt0iOlEVBXViE7IRdTZbETH56C48sqFGRZyGe4Kc8eUfj7o6nHjCVGJqHUZRLDz9/dHQUEBRo0ahUmTJmHs2LE3nU3ZkDHYEelPQWkVfj2Sih8PJiO1oFy3PNjVGpGhLhgZ6oquHjYd+j7OVWotDibl684tzCyq0K3r4WWLKX19MC7MjaN4RHpgEMEOAE6ePImNGzdi48aNOHnyJAYMGICJEydiwoQJ8PX11VdZrYLBjqhtCSEQm1qIH/Yn469Tmbo55WzMTHB/by88HOHNCweuQwiBw5cu44cDydh8OhPVmpo/E3YWpnig9mfn42Cp5yqJOg6DCXZXy8jI0IW8nTt3IjAwUBfyevfure/ybhuDHVHbKKtS48/jGfh+fzLOZl65UKCrhw0e6+uLu7q7w1zOUaemyi2urBntPJCMjNpRPIkEGNzZCVP6+mBYsDNkvOCCqFUZZLC7WmlpKTZv3oyNGzfin3/+wdy5c/HKK6/ou6zbwmBH1Lou5JTghwPJWHcsTTeJr9xEqjtPrLunskMfar1dGq3AjvgcfH8gGbvO5eqWe9ia4+EIb0y+w4vz4xG1EoMPdlfTarXIz8+Hk5OTvku5LQx2RK3jeGohPt52DjsTroQNHwcLPBrhg/vCPdtsfrmO5FJeKX46lIJfj6SisKwaAGAqk+C+cC88PawTPO0s9FwhkXExuGB36NAhREdHIycnB1rtlXsrSiQSfPDBB3qsrOUw2BG1rGsDnVQCDA92wZR+PhgU4Mj52NpARbUGf53MxPcHknEitRBATcC7v7cXZg9lwCNqKQYV7BYuXIj/+7//Q1BQEFxcXOodKpFIJNixY4ceq2s5DHZELePaQCeTSjCphweeGR4AP0ee0K8vh5IK8PH2c9h7IR8AAx5RSzKoYOfi4oIlS5Zg2rRp+iyj1THYEd2e6wW6Z4cHwJeBrt04mJiPj7efx76LDHhELcWggp2bmxt27dqFzp0767OMVsdgR3RrGOgM0/UC3tPDAuBha67n6ogMi0EFu6VLlyIjIwPLli3TZxmtjsGOqHlOpBbi4+3nsSM+BwADnaFqLOA90NsLsxnwiJrMoIKdVqvFuHHjcO7cOYSGhja4xdj69ev1VFnLYrAjaprE3BIs2hyPqLPZABjojEVjAe/Rvj54fkRn2FrwymWiG2lOhjBpo5qu69lnn8XOnTsxbNgwODg4cJ4pog6qsKwKn2y/gO/2X4JaKxjojEyEvwN+8neoF/BW772E9cfSMefOzni0rw9MZcZ/f16i1qb3ETtra2v88ssvGDdunD7LaHUcsSNqXLVGix8OJOPj7ed1c6INC3LCq+NCEOBsrefqqLXsPp+Ld/6KQ0J2MQDA39ESr4wNwYgQZ37AJ7qGQY3Y2dvbo1OnTvoug4jamBAC2+NysPCfOCTmlQIAglys8eq4EAwONOwJyenmBnV2wt/POeDXI2n4MCoBiXmleOK7IxgQ4IBXx4Yi1J0fgIluhd5H7FavXo0tW7Zg9erVsLAw3kvhOWJHdEVcpgrv/H1WN+eZg6UccyMDMbm3F0x4OK7DKa6oxvLoi/h6TxKq1FpIJMDk3l6YGxkIZ2szfZdHpHcGdfFEz549cfHiRQgh4Ovr2+DiiWPHjumpspbFYEcE5BRX4MOt5/DrkVRoBSCXSTF9oB+eHtYJ1mamN98AGbXUgjIs2RKPv05mAgAs5TLMHhaAGQP9YGYq03N1RPpjUIdiJ02apO8SiKiVVVRr8PWeJCzfeQGlVRoAwLgwN7w8Ohhe9sY7Uk/N42Vvgc8e7oXHBxTgrb/icCK1EO/9m4CfDqbgxdFBmNDdneffEd2E3kfsOgqO2FFHtT0uG29uOoPUgnIAQHdPJV4bH4revvZ6rozaM61WYNPJDCzZHI+MogoAwB2+dnh7UlcEu/J3KHUsBnUotqNgsKOOJrWgDAs2ncW2uJr56FxtzPDymGBM6O4OqZSjLtQ05VUafL0nEZ/vvIjyag1kUgmm9ffFCyMDYaXQ+0EnojbR7oOdvb09zp07B0dHxya19/b2xu7du+Hj49PKlbUeBjvqKCrVGny5KxGf7byAimotTKQSzBjkh+eGd4Yl/xDTLcooLMfbf53F5tNZAAAXGwVeHReKu8LceHiWjF67P8eusLAQmzdvhlKpbFL7/Px8aDSaVq6KiG7X7vO5eOPPM7rpS/r62+PtiV3R2YXz0dHtcbc1x4pHwxFzLhdv/Hkal/LL8NzPsVh7OAULJnRFgLOVvkskahf0MmInlTZ/OoMLFy7A39+/FappGxyxI2OWVVSBt/8+i79rr2Z0tFLgtfEhPNmdWkVFtQardiXi850XUKnWwlQmwcxB/nhmeAAs5BwVJuPT7g/FdkQMdmSMqjVarNl7Ccu2nUNplQZSCfBYP1/MjQyEDacvoVaWkl+GNzedwY74HACAh605Xr8rFJGhLvxAQUalORnC6GYC3bVrF+666y64u9eMFPzxxx/11gsh8Oabb8Ld3R3m5uYYOnQozpw5c8NtnjlzBvfeey98fX0hkUiwbNmy1tsBIgNxMDEf4z7ZjXf/iUNplQa9vG2x6dmBeHNCF4Y6ahPeDhb4empvrJoSDg9bc6QXluPJ749i+prDSM4v1Xd5RHphdMGutLQU3bt3x2effdbo+qVLl+LDDz/EZ599hsOHD8PV1RUjR45EcXHxdbdZVlYGf39/LF68GK6urq1VOpFByC+pxNxfj2PyqgM4l10Ce0s5lt4Xht9n9UcX96adN0vUUiQSCSK7uGLb3CF4elgnmMok2JmQi5Ef7cLH286jUs3zs6ljMepDsRKJBBs2bNBNgiyEgLu7O+bMmYOXXnoJAFBZWQkXFxcsWbIETz755E236evrizlz5mDOnDnNqoWHYsnQabUCvx5JxaLN8Sgqr4ZEAjzUxxsvjgqCrYVc3+URAQAu5pbgjT/PYM+FPACAv5Ml3p3UDf06Oei5MqJb16EPxd5IUlISsrKyEBkZqVumUCgwZMgQ7Nu3r0Xfq7KyEiqVqt6DyFCdyy7G5FX78fL6Uygqr0aomw3WP9UfC+/uxlBH7UonJyt8P6MPPnmoJxytFEjMLcVDXx7A3F+PI7+kUt/lEbW6DhXssrJq5z9ycam33MXFRbeupSxatAhKpVL38PLyatHtE7WF8ioNlmyJx9iPd+PwpcuwkMvwf+NCsPGZAejpbafv8ogaJZFIMKG7O7bPG4JH+3pDIgHWH0vHiA9jsPZwCrRaoz1QRaT/YDd06FB89913KC8vb7P3vPZqKSFEi19BNX/+fBQVFekeqampLbp9ota2MyEHkctisCL6ItRagZGhLoiaOwRPDPKHiUzvvzqIbkppbop3JnXD+qf6I8TNBoVl1Xhp3SlMXrUf57Kvf141kSHT+2/n8PBwvPjii3B1dcXMmTNx4MCBVnuvugsfrh2dy8nJaTCKd7sUCgVsbGzqPYgMQbaqAk//eAyPrz6M1IJyuCvNsGpKOL58rDc8bM31XR5Rs/X0tsOmZwbg/8aFwEIuw+FLlzH2491YuiUe5VW8uIKMi96D3QcffID09HR89913yM3NxeDBgxEaGor3338f2dnZLfpefn5+cHV1RVRUlG5ZVVUVYmJi0L9//xZ9LyJDo9EKfLvvEu78IAZ/n8qETCrBEwP9EDV3CCK78GpwMmwmMimeGOSPqLlDMDLUBWqtwPLoi4hcFoPohBx9l0fUYvQe7ABAJpNh4sSJ+OOPP5Ceno6HH34Yr732Gry8vDBp0iTs2LGjydsqKSnB8ePHcfz4cQA1F0wcP34cKSkpkEgkmDNnDhYuXIgNGzbg9OnTmDZtGiwsLPDwww/rtvHYY49h/vz5uudVVVW6bVZVVSE9PR3Hjx/HhQsXWuxnQKRPp9OLcM/yvXhj4xkUV6rR3csWG58ZgP8bH8r7u5JR8bA1x5eP9cbKKeFwU5ohtaAc01YfxtM/HUOOqkLf5RHdtnY13cmhQ4ewevVq/Pzzz1AqlZg2bRoyMzPx448/4qmnnsL7779/021ER0dj2LBhDZZPnToVa9asgRACCxYswMqVK3H58mVERETg888/R9euXXVthw4dCl9fX6xZswYAcOnSJfj5+TXY5pAhQxAdHd2kfeN0J9QeqSqq8eHWc/hu/yVoBWCtMMGLo4PwcIQPZFLO3E/GrbRSjY+izmH1vkvQaAWsFCaYFxmIKX19eB4ptSsGdUuxnJwcfP/991i9ejXOnz+Pu+66C0888QRGjRqlu6Bh27ZtmDRpEkpKSvRZ6m1hsKP2RAiBjScy8M7fccgtrpkCYnyYG14fHwpnGzM9V0fUts5kFOGVDadxIrUQANDF3QbvTOrKK7+p3TCoYCeXy9GpUydMnz4d06ZNg5OTU4M2KpUKEydOxM6dO/VQYctgsKP24mJuCV7/8zT2XsgHAPg5WuKtiV0wqHPD/3tEHYVWK/DL4VQs2XJlAu4H7/DGS6M5ATfpn0EFu927d2PQoEH6LKFNMNiRvlVUa/D5zgtYGZOIKo0WChMpnhkWgP8M8YfCRKbv8ojahbySSizeHI/fj6YBAOwt5Zg/Jhj3hXu2+LRYRE1lUMFu+PDhWL9+PWxtbestV6lUzb5woj1jsCN92hGfjTc2nkFqQc18kUODnPDWhK7wdrDQc2VE7dOhpAL83x+ncC675hSgO3zt8M6kbghytdZzZdQRGVSwk8lkyMzMhLOzc73lOTk58PDwQHV1tZ4qa1kMdqQPGYXlWLDpDP49UzN1kJvSDG/cFYpRXVw5+kB0E9UaLb7Zk4Rl286jvFoDmVSCGQP98PyIzrxanNpUczKE3v5lnjx5EkDNSdxnz56tN2mwRqPBli1b4OHhoa/yiAxa3R+kj7efR1mVBia1f5Ce4x8koiYzlUnx5JBOGN/dHW/VfkBatSsRf53IwOt3dcGoLi78gETtjt5G7KRSqe4/RGMlmJub49NPP8X06dPburRWwRE7aiu7z+firU1ncT6Hh5CIWtK1pzQMDnTC6+NDEODM/1vUugziUGxycjKEEPD398ehQ4fqXQ0rl8vh7OwMmcx4TuhmsKPWdimvFO/8HYdtcTWHXXnSN1HLK6/SYHn0lYuQZFIJHuvngzkjAqG0MNV3eWSkDCLYdTQMdtRaiiuq8dnOC/hmTxKqNQImUgke6+eL50d05h8aolZyKa8U7/4Th6izNR+k7CxMMS8yCA/18ebk3tTi2n2w27hxI8aMGQNTU1Ns3Ljxhm0nTJjQRlW1LgY7amlarcDvR9Ow9N8E5JXUTDI8JNAJr40PRYCzlZ6rI+oYrj31IdjVGq/fFYr+nRz1XBkZk3Yf7KRSKbKysuDs7Ayp9Pq3bZFIJNBoNG1YWethsKOWdORSARZsOotT6UUAAH9HS7w2PhTDgp1v8koiamlqjRY/HkzBh1HnUFReM5PD6C6ueHVcCLzsOaUQ3b52H+w6IgY7agkZheVYvDkeG09kAKi5t+vzd3bGY/18ITfhvS2J9OlyaRWWbTuHHw6mQKMVkJtIMXOQH2YPDeDV6HRbGOzaIQY7uh3lVRqs3HURX8RcREW1tvZ2R16YFxkERyuFvssjoqskZBXjrb/O6G7b52ytwMtjgjGphwekPP+OboFBBbvnnnsOAQEBeO655+ot/+yzz3DhwgUsW7ZMP4W1MAY7uhXVGi1+O5KGT7afR5aqAgDQx88er48PRVcPpZ6rI6LrEUIg6mw23vk7DikFZQCArh42+G9kEIYEOvFKdWoWgwp2Hh4e2LhxI8LDw+stP3bsGCZMmIC0tDQ9VdayGOyoObRagU0nM/Bh1Dkk59f8UfCwNccrY0MwthvvGkFkKCrVGnyz5xI+33kBJZVqAEAfX3v8b3QQ7vC113N1ZCgMKtiZmZnh9OnTCAgIqLf8woUL6Nq1KyoqKvRUWctisKOmEEJgW1wOPtiagPisYgCAo5UczwwLwEMR3lCYGM/cjkQdSUFpFVZEX8C3+5NRpdYCqLln838jgzj6TjdlELcUqxMQEIAtW7bgmWeeqbd88+bN8Pf311NVRG1v34U8LP03AcdTCwEANmYmeHJIJ0zr78sTr4kMnL2lHK+OC8X0gX74dMcF/Ho4FdEJuYhOyMW4bm54YWQgpymiFqH3vxZz587FM888g9zcXAwfPhwAsH37dnzwwQdGc34d0Y3EplzG+1sTdCdam5vK8PgAXzw5uBMnGCYyMm5Kcyy8uxv+M8gfy7adw58nMvD3qUxsPp2Je3t54vk7O8PTjlOk0K3T+6FYAFixYgXeffddZGTUTOHg6+uLN998E4899pieK2s5PBRL14rPUuGDred0M9ebyiR4JMIHs4d1grO1mZ6rI6K2cO3vAblMiocjvPH0sAA4WfOKd6phUOfYXS03Nxfm5uawsjK+4WgGO6pzKq0IK3ddxN+nMiEEIJWAn9SJOrjGRu4fifDG9IF+cLc113N1pG8GGexyc3ORkJAAiUSCoKAgODoa1+1YGOw6Nq1WIOZcLlbtSsT+xHzdcp5bQ0RX23shD+9dda6tiVSC8WFueGKQPy+y6MAMKtiVlpbi2WefxXfffQettuZKIZlMhsceewyffvopLCyMYwSDwa5jqlRr8GdsBr7cnai7l6SJVIK7urtj5iB/hLrz3wIR1SeEQPS5XHy5KxH7Ll75IDggwAEzB/lzHrwOyKCC3ZNPPolt27bhs88+w4ABAwAAe/bswXPPPYeRI0dixYoV+iyvxTDYdSyFZVX48WAKVu+9hLySSgCAlcIED0d4Y1p/Xx5aIaImOZ1ehC93J+Kvk5nQaGv+XAe5WOOJQX6Y0MOdUyB1EAYV7BwdHfH7779j6NCh9Zbv3LkTDzzwAHJzc/VTWAtjsOsYUvLL8M3eJKw9nIryag0AwE1phukD/DC5jxdszHiVKxE1X3phOVbvScLPh1JQWlXzu8XZWoFpA3zxSB8fXkFv5Awq2FlYWODo0aMICQmpt/zMmTPo06cPSktL9VRZy2KwM15CCBxNvozVey9h8+lM1H6oRqibDf4z2B/jwtxgKpPqt0giMgpF5dX45VDN0YC62wxayGV4oLcXpvb3hZ+jpZ4rpNZgUMFuxIgRcHBwwHfffQczs5opHsrLyzF16lQUFBRg27Zt+iyvxTDYGZ/0wnJsOJaGdcfSkZR35QPIkEAn/GewP/p3cuB5METUKqrUWvx1MgOrdiXq7lIDAOE+dri3lyfGhblBac5RPGNhUMHu9OnTGD16NCoqKtC9e3dIJBIcP34cZmZm+Pfff9GlSxd9ltdiGOyMQ1mVGptPZWHdsTTsT8xH3f8eC7kM47q5YcYgPwS7sn+JqG0IIbDnQh6+2ZOEmHO5uiMGchMpRnVxxb29PDCosxNkUn7INGQGFeyAmhG6H374AfHx8RBCIDQ0FI888gjMzY3nBHMGO8Ol1QocTCrAumNp2HwqU3d+CwD083fAveGeGNPVlbf9IiK9ylFV4I/j6fj9aBrOZZfoljtbK3B3Lw/c18sTnV2s9Vgh3SqDC3YdAYOd4UnOL8W6Y+lYfywNaZfLdct9HCxwby9P3N3TA172xjEdDxEZDyEETqersO5YGv48no7LZdW6dWGeStzbyxMTurvDzlKuxyqpOdp9sNu4cWOT206YMKEVK2k7DHbtn1YrcDqjCDvjc7EzIUc3QSgAWCtMMC7MDfeFeyLcx47nzhGRQahSa7EjPgfrjqVhZ3wO1LXHak1lEgwIcMTQQCcMDXKGLy+6aNfafbCTSpt2haBEIoFGo7l5QwPAYNc+FZZVYdf5PEQn5GDXuVzklVTp1kkkwMAAR9wX7olRXVxhZsr5oojIcOWXVGLjiQz8fjQNZzJU9db5OVpiSKAThgU7I8LPnr/v2pl2H+w6Iga79kGrFTibqUJ0Qg52JuQiNuWy7mRjoGYS4QEBDhga5Izhwc5wsTHTX7FERK3kfHYxdsTnIDohF4cvFehG8gDAzFSK/p0cMTTICcOCnHnKSTtgsMGuoqJCN+WJsWGw0w+tVuBSfilOphVhz4U8xJzLRW5xZb02gS5WGBbkjCFBTujtYw+5CeecI6KOo7iiGnsv5CM6oSbo1c2PV8ffyRJDA53R198eYZ62cFUa59/p9syggp1Go8HChQvxxRdfIDs7G+fOnYO/vz9ee+01+Pr6YsaMGfosr8Uw2LU+IQTSLpfjZFoRTqYV4mRaEU6nF6G4Ul2vnYVcVnNuSVDNuSUevL0XERGAmt+jCdnF2Bmfi+iEHBxJvqy7lVkdZ2sFwjyV6OZhizAvJcI8lHCwUuip4o7BoILdW2+9hW+//RZvvfUWZs6cidOnT8Pf3x+//vorPvroI+zfv1+f5bUYBruWJYRAtqoSJ9IKcSqtCCfTi3AqrbDe1V91FCZSdHG3QbiPHYYGOaO3rx3vr0hE1ASqimrsPV9ztON4aiHOZRdD20hq8LA1rwl7nkqEediim4eStzlrQQYV7AICArBy5UqMGDEC1tbWOHHiBPz9/REfH49+/frh8uXLzdrerl278N577+Ho0aPIzMzEhg0bMGnSJN16IQQWLFiAVatW4fLly4iIiMDnn39+04mQ161bh9deew0XL15Ep06d8O677+Luu+9ucl0Mds1XpdYio7AcqZfLkFJQhtSCcqQWlOmeFzYS4kxlEgS72iDMU6n7RBnoYgUT3tKLiOi2lVdpcDazCCdSi3AqvQgn0gqRmNv4rT9dbBTwsrOAt70FPO1rvnrZmcPbwQIu1maQctLkJmtOhtD7jKrp6ekICAhosFyr1aK6uuEf7pspLS1F9+7d8fjjj+Pee+9tsH7p0qX48MMPsWbNGgQGBuKdd97ByJEjkZCQAGvrxidu3L9/PyZPnoy3334bd999NzZs2IAHHngAe/bsQURERLNr7OiqNVoUlVejsKwahWVVKCyrxuWyKmQVVdQLcZlF5Y1+MqwjlQCBLta1nxJt0d1TiSBXa47GERG1EnO5DOE+9gj3sdctK66oxul0Vc0pMOk1p8KkFpQjW1WJbFUljiQ3HKCRy6TwtDOHl70FvOzN4W1vAWdrMygtTGFrbgo7CzlsLUxhY2bKANhMeh+x6927N+bMmYNHH3203ojdggULsG3bNuzevfuWty2RSOqN2Akh4O7ujjlz5uCll14CAFRWVsLFxQVLlizBk08+2eh2Jk+eDJVKhc2bN+uWjR49GnZ2dvj555+bVEtrjtipNVqUXHMeWZ3r9a5Azc9DK6581QoBrRAQuu9R+7zm+yq1FlUaLSqrtahUa1Cp1tY8qjVXLb+yrqRCjctlVSgqrwluhWXVKCqrbnDO240oTKTwuuqTXs0vgZrnvg6WMJczxBERtTeFZVW4lF+G1IKaD+tpV31oTy8sb3De3vVIJIDSvCbs2daGvbrvLRUyKExkUJhIoTCRQl73van0muU1z01lEkgkEkglgFQigVQigUQCSKVXlkmuXneTuhpja9E6kz4b1IjdG2+8gSlTpiA9PR1arRbr169HQkICvvvuO/z1118t+l5JSUnIyspCZGSkbplCocCQIUOwb9++6wa7/fv344UXXqi3bNSoUVi2bNl136uyshKVlVeuvlSpVNdte7vOZKgw8fO9rbb91mJjZgJbCznsLEyhtJDD2VpRE+BqP7152VnAyVrByYCJiAyMrYUcPSzk6OFl22CdWqNFZlFFvVNrUgvKkV9aWXskp+ZoTmmVBkJAtwz5ZW2/I80gk0pwceFYfZeh/2B31113Ye3atVi4cCEkEglef/119OrVC5s2bcLIkSNb9L2ysrIAAC4uLvWWu7i4IDk5+Yava+w1ddtrzKJFi7BgwYLbqLZtXPl0gsY/yVy1zlQm0X0Kktd+ElKYyGo/HV31aal2vbXCBMra4GZrUftpq/aTltLclDelJiLqgExkUt3RlxupUmtRWF6ForJqXK47dae85uvlsmqUV2l0R4mq6o4g1R5FqlRra5ddObqk0dYcldJqGzsydeWoVRMHE9stvQc7oGb0a9SoUW32fteOAAkhbjoq1NzXzJ8/H3PnztU9V6lU8PLyuoVqby7MU3nDTwnXq1IiabhfRERE7YHcRApnazM4W7f9vHnaG6S7661pL9MC6/1Swccffxzbt29vkx+Iq6srADQYacvJyWkwInft65r7GoVCARsbm3qP1iKRSCCTXv8hvc6DoY6IiKih6/3dlN7gb217mX1B7yN2+fn5GDduHBwcHPDggw/i0UcfRc+ePVvlvfz8/ODq6oqoqCjde1RVVSEmJgZLliy57uv69euHqKioeufZbd26Ff3792/ye9cF19Y8146IiIiMT112aNIgmGgHLl++LFauXCmGDBkipFKpCAkJEe+++65ISkpq9raKi4tFbGysiI2NFQDEhx9+KGJjY0VycrIQQojFixcLpVIp1q9fL06dOiUeeugh4ebmJlQqlW4bU6ZMES+//LLu+d69e4VMJhOLFy8WcXFxYvHixcLExEQcOHCgyXWlpqYK1F6MygcffPDBBx988NHcR2pq6k3zht6nO7lWWloafv75Z3zzzTc4f/481OqmT40BANHR0Rg2bFiD5VOnTsWaNWt0ExSvXLmy3gTFXbt21bUdOnQofH19sWbNGt2y33//Hf/3f/+HxMRE3QTF99xzT5Pr0mq1yMjIgLW1dascAq07hy81NbVDTIDM/TVu3F/j19H2mftr3Fp7f4UQKC4uhru7O6TSGx/ybVfBrrq6Gn///Td++OEH/P3337C3t0d6erq+yzIIHe3OFtxf48b9NX4dbZ+5v8atPe1vuzjTb+fOnZg5cyZcXFwwdepUWFtbY9OmTUhNTdV3aUREREQGQ+8XT3h6eiI/Px+jRo3CypUrcdddd8HMrO0vbSYiIiIydHoPdq+//jruv/9+2NnZ6bsUg6ZQKPDGG29AoVDou5Q2wf01btxf49fR9pn7a9za0/62q3PsiIiIiOjWtYtz7IiIiIjo9jHYERERERkJBjsiIiIiI8FgR0RERGQkGOwMyPLly+Hn5wczMzOEh4dj9+7dN2wfExOD8PBwmJmZwd/fH1988UUbVdoymrO/0dHRkEgkDR7x8fFtWPGt27VrF+666y64u7tDIpHgjz/+uOlrDLl/m7u/hty/ixYtwh133AFra2s4Oztj0qRJSEhIuOnrDLV/b2V/Dbl/AWDFihUICwuDjY0NbGxs0K9fP2zevPmGrzHU/gWav7+G3r/XWrRoESQSCebMmXPDdvrqYwY7A7F27VrMmTMHr776KmJjYzFo0CCMGTMGKSkpjbZPSkrC2LFjMWjQIMTGxuKVV17Bc889h3Xr1rVx5bemuftbJyEhAZmZmbpH586d26ji21NaWoru3bvjs88+a1J7Q+/f5u5vHUPs35iYGDz99NM4cOAAoqKioFarERkZidLS0uu+xpD791b2t44h9i9QMx/r4sWLceTIERw5cgTDhw/HxIkTcebMmUbbG3L/As3f3zqG2r9XO3z4MFatWoWwsLAbttNrHzf5LvakV3369BGzZs2qtyw4OFi8/PLLjbZ/8cUXRXBwcL1lTz75pOjbt2+r1diSmru/O3fuFADE5cuX26C61gVAbNiw4YZtDL1/r9aU/TWm/s3JyREARExMzHXbGFP/NmV/jal/69jZ2Ymvvvqq0XXG1L91brS/xtK/xcXFonPnziIqKkoMGTJEPP/889dtq88+5oidAaiqqsLRo0cRGRlZb3lkZCT27dvX6Gv279/foP2oUaNw5MgRVFdXt1qtLeFW9rdOz5494ebmhhEjRmDnzp2tWaZeGXL/3g5j6N+ioiIAgL29/XXbGFP/NmV/6xhD/2o0Gvzyyy8oLS1Fv379Gm1jTP3blP2tY+j9+/TTT2PcuHG48847b9pWn33MYGcA8vLyoNFo4OLiUm+5i4sLsrKyGn1NVlZWo+3VajXy8vJardaWcCv76+bmhlWrVmHdunVYv349goKCMGLECOzatastSm5zhty/t8JY+lcIgblz52LgwIHo2rXrddsZS/82dX+NoX9PnToFKysrKBQKzJo1Cxs2bEBoaGijbY2hf5uzv8bQv7/88guOHTuGRYsWNam9PvtY77cUo6aTSCT1ngshGiy7WfvGlrdXzdnfoKAgBAUF6Z7369cPqampeP/99zF48OBWrVNfDL1/m8NY+veZZ57ByZMnsWfPnpu2NYb+ber+GkP/BgUF4fjx4ygsLMS6deswdepUxMTEXDfsGHr/Nmd/Db1/U1NT8fzzz2Pr1q3Nupe9vvqYI3YGwNHRETKZrMFoVU5OToNPBHVcXV0bbW9iYgIHB4dWq7Ul3Mr+NqZv3744f/58S5fXLhhy/7YUQ+vfZ599Fhs3bsTOnTvh6el5w7bG0L/N2d/GGFr/yuVyBAQEoHfv3li0aBG6d++Ojz/+uNG2xtC/zdnfxhhS/x49ehQ5OTkIDw+HiYkJTExMEBMTg08++QQmJibQaDQNXqPPPmawMwByuRzh4eGIioqqtzwqKgr9+/dv9DX9+vVr0H7r1q3o3bs3TE1NW63WlnAr+9uY2NhYuLm5tXR57YIh929LMZT+FULgmWeewfr167Fjxw74+fnd9DWG3L+3sr+NMZT+vR4hBCorKxtdZ8j9ez032t/GGFL/jhgxAqdOncLx48d1j969e+ORRx7B8ePHIZPJGrxGr33c6pdnUIv45ZdfhKmpqfj666/F2bNnxZw5c4SlpaW4dOmSEEKIl19+WUyZMkXXPjExUVhYWIgXXnhBnD17Vnz99dfC1NRU/P777/rahWZp7v5+9NFHYsOGDeLcuXPi9OnT4uWXXxYAxLp16/S1C81SXFwsYmNjRWxsrAAgPvzwQxEbGyuSk5OFEMbXv83dX0Pu36eeekoolUoRHR0tMjMzdY+ysjJdG2Pq31vZX0PuXyGEmD9/vti1a5dISkoSJ0+eFK+88oqQSqVi69atQgjj6l8hmr+/ht6/jbn2qtj21McMdgbk888/Fz4+PkIul4tevXrVmz5g6tSpYsiQIfXaR0dHi549ewq5XC58fX3FihUr2rji29Oc/V2yZIno1KmTMDMzE3Z2dmLgwIHi77//1kPVt6ZuOoBrH1OnThVCGF//Nnd/Dbl/G9tPAGL16tW6NsbUv7eyv4bcv0IIMX36dN3vKicnJzFixAhdyBHCuPpXiObvr6H3b2OuDXbtqY8lQtSezUdEREREBo3n2BEREREZCQY7IiIiIiPBYEdERERkJBjsiIiIiIwEgx0RERGRkWCwIyIiIjISDHZERERERoLBjoiIiMhIMNgREbUSX19fSCQSSCQSFBYWtsl71r2fra1tm7wfEbUvDHZERM00dOhQzJkzp0lt33rrLWRmZkKpVLZuUbUyMzOxbNmyNnkvImp/TPRdABGRMbO2toarq2ubvZ+rq2ubhUgian84YkdE1AzTpk1DTEwMPv74Y91hz0uXLjX59cnJybjrrrtgZ2cHS0tLdOnSBf/8849u/dmzZzF27FhYWVnBxcUFU6ZMQV5enm69VqvFkiVLEBAQAIVCAW9vb7z77rstuYtEZMAY7IiImuHjjz9Gv379MHPmTGRmZiIzMxNeXl5Nfv3TTz+NyspK7Nq1C6dOncKSJUtgZWUFoOYw6pAhQ9CjRw8cOXIEW7ZsQXZ2Nh544AHd6+fPn48lS5bgtddew9mzZ/HTTz/BxcWlxfeTiAwTD8USETWDUqmEXC6HhYXFLR1iTUlJwb333otu3boBAPz9/XXrVqxYgV69emHhwoW6Zd988w28vLxw7tw5uLm54eOPP8Znn32GqVOnAgA6deqEgQMH3uZeEZGxYLAjImpDzz33HJ566ils3boVd955J+69916EhYUBAI4ePYqdO3fqRvCudvHiRRQWFqKyshIjRoxo67KJyEDwUCwRURt64oknkJiYiClTpuDUqVPo3bs3Pv30UwA158/dddddOH78eL3H+fPnMXjwYJibm+u5eiJq7xjsiIiaSS6XQ6PR3PLrvby8MGvWLKxfvx7z5s3Dl19+CQDo1asXzpw5A19fXwQEBNR7WFpaonPnzjA3N8f27dtbaleIyMgw2BERNZOvry8OHjyIS5cuIS8vD1qttsmvnTNnDv79918kJSXh2LFj2LFjB0JCQgDUXFhRUFCAhx56CIcOHUJiYiK2bt2K6dOnQ6PRwMzMDC+99BJefPFFfPfdd7h48SIOHDiAr7/+urV2lYgMDIMdEVEz/fe//4VMJkNoaCicnJyQkpLS5NdqNBo8/fTTCAkJwejRoxEUFITly5cDANzd3bF3715oNBqMGjUKXbt2xfPPPw+lUgmptObX9WuvvYZ58+bh9ddfR0hICCZPnoycnJxW2U8iMjwSIYTQdxFERMbI19cXc+bMafJdKlrKmjVrMGfOnDa7jRkRtR8MdkRErcTX1xeZmZkwNTVFenp6m9wRwsrKCmq1GmZmZgx2RB0QpzshImolMTExqK6uBlBza7G2cPz4cQCATCZrk/cjovaFI3ZERERERoIXTxAREREZCQY7IiIiIiPBYEdERERkJBjsiIiIiIxEk66KValUzd6wjY1Ns19DRERERLeuSVfFSqVSSCSSpm9UIsG5c+fg7+9/W8URERERUdM1eR6733//Hfb29jdtJ4TA2LFjb6soIiIiImq+JgU7Hx8fDB48GA4ODk3aqL+/P0xNTW+rMCIiIiJqHk5QTERERGQkWuSqWN6PkIiIiEj/mh3slixZgrVr1+qeP/DAA3BwcICHhwdOnDjRosURERERUdM1O9itXLkSXl5eAICoqChERUVh8+bNGDNmDP73v/+1eIFERERE1DRNviq2TmZmpi7Y/fXXX3jggQcQGRkJX19fREREtHiBxkKr1SIjIwPW1tbNmjqGiIiIOjYhBIqLi+Hu7g6p9MZjcs0OdnZ2dkhNTYWXlxe2bNmCd955R/emGo3m1iruADIyMnSBmIiIiKi5UlNT4enpecM2zQ5299xzDx5++GF07twZ+fn5GDNmDADg+PHjCAgIuLVKOwBra2sANZ3Cu3IQERFRU6lUKnh5eemyxI00O9h99NFH8PX1RWpqKpYuXQorKysANYdoZ8+e3fxqO4i6w682NjYMdkRERNRsTTmVq8nz2L3yyiuYNGkS+vTpc9uFdUQqlQpKpRJFRUUMdu2cEAJ5JVXIKa5AUXk1VOVqqCqqoSqvfVSoa5dXQ1VRrWtTpdFCJpXARCqB7KpHzXMpTKQSSK9abyGXwcFSAUcrORys5HCwVMDBSg5Hq5qv9pZyKExk+v5xEBGRnjUnQzR5xC4zMxPjx4+HTCbDXXfdhUmTJmHEiBFQKBS3XTCRPpRVqZGYW4qkvJpHYm5Jzde8UhRXqPVdHgDA2sykJuhZyuGiNIO/oyX8HC3h72QFP0dLKM15hxciIrqiWXeeEEJgz5492LRpEzZu3Ij09HSMHDkSEyZMwPjx4+Ho6NiatRo0jtjpT1mVGrEphYjLVNUGuJogl6WquO5rJBLA0UoBpbkpbMxMYGNuWvt97VdzE93zunVyEyk0WgGNVkCtFdBotdBoAbVWe2WZpm6dQGmlGvmlVcgvqUR+aRXySiqRX1KF/NKar2rtzf9rOlrJa4KeoxX8nCzh72gJfydLeNtbQm7SIvOPExGRnjUnQ9zWLcXi4uKwadMm/Pnnnzhy5AgiIiIwYcIEPPTQQ/Dw8LjVzRolBru2U1RejSOXCnAoqQAHkwpwOr3ouiHJ3rImGPnVBiL/2tEwb3sLmJnq7zCoEAJF5dXIK6kJfnklVcgsKsfF3FIk5ZUgMbcUOcWV1329VAL4Oliim6cSYZ626O6pRKi7DSzkzT6tloiI9KzNgt3VcnJydCN5gwYNwn//+9+W2KzRYLBrPXkllThcG+IOJRUgLkuFa/9VuynN0MPLtja8XRndsrWQ66foFlBSqUZSbikS80rqjUQm5pagtKrh1ENSCRDoYo0wTyW61Ya9YFcbjuwREbVzegl2dGMMdi2nrEqNnfG52HMhD4eS8nExt7RBGz9HS/TxtUcfv5qHp515h5kYWgiBnOJKxGWqcCqtCCfSinAyrbDRET65TIpgt5qw18PLDn397eFpZ6GHqomI6HpaPNjdc889TX7z9evXN7ltR8Jgd3sqqjWIOZeLv05mYtvZbJRX1x+RCna11oW4Pr72cLYx01Ol7Ve2qgInUgtxMq0IJ9Nrwl5hWXWDdl725ujn74B+nRzQz98Rrkr+LImI9KnFr4pVKpW674UQ2LBhA5RKJXr37g0AOHr0KAoLC5sVAIlupkqtxd4Ledh0MgNRZ7JRXHnlSlUve3NEhrqir78D7vC1M+hDqm3FxcYMkV1cEdnFFUDN/+XUgnKcTK8Je4cvFeBkWhFSC8qRWpCGX4+kAQD8HS3Rt5MD+vk7oK+/A5yseSU8EVF71exDsS+99BIKCgrwxRdfQCarOblco9Fg9uzZsLGxwXvvvdcqhRo6jtg1jVqjxYHEAvx1MgNbzmTVG1FyV5phXJgbxoe5I8xT2WEOrbalkko1Dl8qwIGL+difmI/T6UW49rqTzs5W6NfJAf07OWJgZ0dYKXhBBhFRa2rVc+ycnJywZ88eBAUF1VuekJCA/v37Iz8/v/kVdwAMdtcnhMCxlEL8EZuOzaczkVdSpVvnaKXA+DA3jA9zQy9vO0ilDHNtqai8GoeTCrCvNujFZarqrTeVSRDh54Bhwc4YEewMX0dLPVVKRGS8WmWC4jpqtRpxcXENgl1cXBy0Wm1zN0cdWLVGi82ns/D17kScSCvSLbezMMWYbjVhLsLPATKGOb1RmpvizlAX3BnqAgC4XFqFg0n52H8xH7vO5yEprxR7LuRhz4U8vP3XWfg7WmJ4sDOGBzujt689r7glImpjzQ52jz/+OKZPn44LFy6gb9++AIADBw5g8eLFePzxx1u8QDI+qopq/HIoBWv2XkJGUc0kwQoTKcaHuWNCD3f07+QAUxkDQXtkZynH6K5uGN3VDQCQmFuCHfE52BGfg0NJBUjMK0XiniR8tScJ1goTDAp0xPBgFwwNcoKjFc/NIyJqbc0+FKvVavH+++/j448/RmZmJgDAzc0Nzz//PObNm6c7747q46FYILWgDKv3XsLawym6edYcreSY0tcXj/b1hgP/8Bs0VUU19pzPw474HOyMz0F+6ZVD6hIJ0MPLFmO6umJMVzd42XNKFSKipmqzeexUqprzbdoyqCxfvhzvvfceMjMz0aVLFyxbtgyDBg26bvuYmBjMnTsXZ86cgbu7O1588UXMmjVLt/7LL7/Ed999h9OnTwMAwsPDsXDhQvTp00fX5s0338SCBQvqbdfFxQVZWVlNrrsjB7tjKZfx1e5EbDmdpTsRP9DFCk8M9MeEHu56vcMDtQ6tVuBkehF2xGVjR0IOTqfXPzevm4cSY7q5YmxXN56XR0R0E616jt3V2jqgrF27FnPmzMHy5csxYMAArFy5EmPGjMHZs2fh7e3doH1SUhLGjh2LmTNn4ocffsDevXsxe/ZsODk54d577wUAREdH46GHHkL//v1hZmaGpUuXIjIyEmfOnKl3W7QuXbpg27ZtuuccmbwxtUaLrWez8dXuRBxLKdQtH9TZEU8M8sfgzo68qtWISaUS9PCyRQ8vW8yNDEJWUQWi4rKx+VQmDiTm41R6EU6lF2HplgSEutlgbDdXjOnmhk5OVvounYjIoN3SiN3vv/+OX3/9FSkpKaiqqqq37tixYy1W3LUiIiLQq1cvrFixQrcsJCQEkyZNwqJFixq0f+mll7Bx40bExcXpls2aNQsnTpzA/v37G30PjUYDOzs7fPbZZ3jssccA1IzY/fHHHzh+/Pgt195RRuyEENh8OgtLt8TjUn4ZgJq7G0zq6Y4ZA/0R5Gqt5wpJ3/JKKrH1TDY2n87Evov50Fw1n0qQi3XNSF43NwS68N8KERHQvAzR7DPUP/nkEzz++ONwdnZGbGws+vTpAwcHByQmJmLMmDG3XPTNVFVV4ejRo4iMjKy3PDIyEvv27Wv0Nfv372/QftSoUThy5AiqqxvOuA8AZWVlqK6uhr29fb3l58+fh7u7O/z8/PDggw8iMTHxhvVWVlZCpVLVexi7YymXcd8X+zH7x2O4lF8GOwtTPDc8AHteHoal93VnqCMANVPYPBzhje9nRODIq3di6b1hGBrkBBOpBAnZxVi27TwiP9qFOz+MwSfbzyOl9gMCERHdXLMPxS5fvhyrVq3CQw89hG+//RYvvvgi/P398frrr6OgoKA1agQA5OXlQaPRwMXFpd7yG53rlpWV1Wh7tVqNvLw8uLm5NXjNyy+/DA8PD9x55526ZREREfjuu+8QGBiI7OxsvPPOO+jfvz/OnDkDBweHRt970aJFDc7LM1apBWVYvCUef5+suZjG3FSG/wz2x38G+8OSk9fSDdhZyvHAHV544A4vFJVV6w7X7j6fhws5Jfgw6hw+jDqHXt62mNTTA+O6ufEiGyKiG2j2X92UlBT0798fAGBubo7i4mIAwJQpU9C3b1989tlnLVvhNa49L0sIccNztRpr39hyAFi6dCl+/vlnREdHw8zsyv0xrx6J7NatG/r164dOnTrh22+/xdy5cxt93/nz59dbp1Kp4OXldYM9MzxFZdX4bOd5fLsvGVUaLSQS4P5wT8yLDIIL79VKzaS0MMV94Z64L9wTqopqbD2TjT+Pp2PvhTwcSynEsZRCvLXpLAZ1dsSknh4YGeoCCzk/OBARXa3ZvxVdXV2Rn58PHx8f+Pj44MCBA+jevTuSkpJwGxfY3pSjoyNkMlmD0bmcnJwGo3JX19pYexMTkwYjbe+//z4WLlyIbdu2ISws7Ia1WFpaolu3bjh//vx12ygUCigUxjmyUKXW4seDyfh4+3ndLb8GdXbEK2NDEOJmvOcPUtuxMbsS8nJUFdh4IgN/Hs/AqfQi7EzIxc6EXFjIZYgMdcGknh4YGOAIE859SETU/GA3fPhwbNq0Cb169cKMGTPwwgsv4Pfff8eRI0dwzz33tEaNAAC5XI7w8HBERUXh7rvv1i2PiorCxIkTG31Nv379sGnTpnrLtm7dit69e8PU1FS37L333sM777yDf//9F717975pLZWVlYiLi7vhNCvGSAiBf89kY/HmON2FEYEuVnhlbAiGBDrxKldqFc42ZnhikD+eGOSPCzkl2Hg8HX8cz0BKQRn+OJ6BP45nwNFKjvFh7rgv3BNd3G34b5GIOqxbmqBYq9XCxKQmE/7666/Ys2cPAgICMGvWLMjl8lYpFKiZ7mTKlCn44osv0K9fP6xatQpffvklzpw5Ax8fH8yfPx/p6en47rvvANRMd9K1a1c8+eSTmDlzJvbv349Zs2bh559/1k13snTpUrz22mv46aefMGDAAN17WVlZwcqqZuqF//73v7jrrrvg7e2NnJwcvPPOO4iJicGpU6fg4+PTpNoN/arYE6mFePfvOBy6VHMepaOVAnNHBuKB3p4cKaE2V3d/4T+Pp+Ovk5kouGoy5GBXa9wX7olJPT14twsiMgqtNkGxWq3Gu+++i+nTp+vtfLHly5dj6dKlyMzMRNeuXfHRRx9h8ODBAIBp06bh0qVLiI6O1rWPiYnBCy+8oJug+KWXXqo3QbGvry+Sk5MbvM8bb7yBN998EwDw4IMPYteuXcjLy4OTkxP69u2Lt99+G6GhoU2u21CDXUW1Bu//m4Cv9yZBCMDMVIqZg/zx5JBOsOKFEdQOVGu02HM+D+uOpWHr2WxUqWvuWW0ilWBYsDPuD/fEsGBn3qaOiAxWq955wsrKCqdPn4avr+/t1NjhGGKwi025jHm/nUBibikAYFIPd7w0JhhuSnM9V0bUuKKyamw8mYHfj6TiRFqRbrmDpRyTenrgvnBPngdKRAanVYPdpEmTMGnSJEybNu12auxwDCnYVao1WLbtPFbGXIRWAM7WCiy6pxtGhDR+kQpRe3Quuxi/H03D+mPpyCup1C3v6mGD+3p5YmIPD9hZtt6pI0RELaVVg93KlSvx5ptv4pFHHkF4eDgsLevf53HChAnNr7gDMJRgdyqtCPN+O45z2SUAgLt7euCNu0Jha8E/gGSYqjVa7DqXi9+OpGF7fDaqNTW/8uQyKSK7uODBO7zRv5MDpFJecEFE7VOrBjup9PrnqUgkEmg0muZsrsNo78GuSq3FZzvO4/Poi9BoBRyt5HhnUjeM7uqq79KIWkxBaRX+PJ6O346k4WzmlbvBeNmbY3JvL9zf24tzMBJRu9OqwY5uTXsOdmczVJj32wnE1f6hGxfmhrcndoU9D1ORETudXoS1h1PxR2w6iivVAACpBBge7IzJd3hjWJATr/gmonaBwa4dao/BrlqjxYroi/hk+3motQJ2FqZ4e1JXjA9z13dpRG2mvEqDf05l4pfDKTh86bJuubO1Avf39sTk3t7wdrDQY4VE1NG1eLD75JNP8J///KfebbZu5IsvvsAjjzwCa2ve9L1Oewt257KLMe/XEziVXnPlYGSoC969uxucrDnvF3VcF3JKsPZwCtYdS683N96AAAdMvsMbo7q4QGEi02OFRNQRtXiwq7uVl5OTU5MKsLGxwfHjx+Hv79+0ijuA9hTsfjuSilf/OI0qtRZKc1MsmNAFE3u4c7Z+olpVai2izmbjl8Mp2HMhD3W/Je0t5bg/3BMP9fGGr6PljTdCRNRCWjzYSaVSdO3aVXe3iZs5deoUEhISGOyu0h6CXZVai3f+Povv9tdMyDw0yAlL7g3jyeJEN5BaUIbfjqRi7ZFUZKuuTJsyIMABD/fxwchQF8hNeC4eEbWeFg92CxYsaHYRzz//PGxtbZv9OmOl72CXU1yBp388pjuH6IU7A/Hs8ABO8UDURGqNFjvic/DToRTEnMvVjeI5Wslxf28vPHQHz8UjotbBiyfaIX0Gu2Mpl/HUD0eRraqEtcIEH03ugTtDOdkw0a1KLSjD2sM1o3i5xVdG8QZ1dsQjEd4YEeLCW5gRUYthsGuH9BXsfjmUgtf/PIMqjRYBzlZYNSUc/k5Wbfb+RMasWqPF9rhs/HgwBbvP5+mWO1sr8EBvLzzYxwuedhzFI6Lbw2DXDrV1sKtUa/DmxrP4+VAKAGB0F1e8/0B3WCmadp4kETVPSn4Zfj6cgt+OpCKvpOaKWqkEGBbkjEf6emNIoDNkPPWBiG5BczKEwR0rWL58Ofz8/GBmZobw8HDs3r37hu1jYmIQHh4OMzMz+Pv744svvmjQZt26dQgNDYVCoUBoaCg2bNhw2++rT9mqCjy46gB+PpQCiQT436ggrHi0F0MdUSvydrDAS6ODse/lEfj84V4YEOAArQC2x+dg+pojGLx0Jz7bcR45xRX6LpWIjJhBBbu1a9dizpw5ePXVVxEbG4tBgwZhzJgxSElJabR9UlISxo4di0GDBiE2NhavvPIKnnvuOaxbt07XZv/+/Zg8eTKmTJmCEydOYMqUKXjggQdw8ODBW35ffTpyqQDjP92D2JRC2JiZ4Jtpd+DpYQGcyoSojchNpBgX5oYfn+iL7fOG4ImBflCamyK9sBzvbz2H/ot24Okfj2HfhTzwgAkRtTSDOhQbERGBXr16YcWKFbplISEhmDRpEhYtWtSg/UsvvYSNGzciLi5Ot2zWrFk4ceIE9u/fDwCYPHkyVCoVNm/erGszevRo2NnZ4eeff76l921Max+KFULgh4MpWLDxDNRagSAXa6x6LBw+Dpxri0jfKqpr7m7xw4FkHEsp1C33d7TEwxHeuC/cE7YWvIUfkSETQrTaIEpzMkSzj83NnTu30eUSiQRmZmYICAjAxIkTYW9v39xN31BVVRWOHj2Kl19+ud7yyMhI7Nu3r9HX7N+/H5GRkfWWjRo1Cl9//TWqq6thamqK/fv344UXXmjQZtmyZbf8vgBQWVmJysorV8upVKrrtr1dFdUavP7nafx6JA1Azb1el94bBkseeiVqF8xMZbinlyfu6eWJsxkq/HgwGX/EpiMxrxTv/B2H9/5NwLgwNzwS4YNe3rYcYScyIBqtwPtbE2AilWBeZJC+y2l+sIuNjcWxY8eg0WgQFBQEIQTOnz8PmUyG4OBgLF++HPPmzcOePXsQGhraYoXm5eVBo9HAxaX+NB0uLi7Iyspq9DVZWVmNtler1cjLy4Obm9t129Rt81beFwAWLVp0S/P/3YqNJzLw65E0SCXAS6OD8Z/B/vzDQNROhbrb4N27u2H+2BD8eTwdPxxIQVymCuuPpWP9sXSEuNngkQhvTOrpwfNiidq5wrIqPPtzrO6q+PFh7ghy1e/tVJt9jt3EiRNx5513IiMjA0ePHsWxY8eQnp6OkSNH4qGHHkJ6ejoGDx7cYBSspVwbWG429NlY+2uXN2WbzX3f+fPno6ioSPdITU29btvbVXeLo2+n98GTQzox1BEZACuFCR6J8ME/zw3Ehtn9cW8vTyhMpIjLVOH//jiNiHe34dUNp3A2o/VG+4no1sVlqnDXZ3uw+3wezEyl+OShnnoPdcAtjNi99957iIqKqneM18bGBm+++SYiIyPx/PPP4/XXX29wCPR2OTo66u5Ze7WcnJwGo2l1XF1dG21vYmICBweHG7ap2+atvC8AKBQKKBSKpu3cbZJIJFh0T7c2eS8ialkSiQQ9ve3Q09sOr40Pwbpj6fjxYDISc0vx48EU/HgwBT29bfFIhA/Gh7nBzFSm75KJOryNJzLw0u8nUV6tgZe9OVY+2huh7vq9D3ydZo/YFRUVIScnp8Hy3Nxc3Xlktra2qKqquv3qriKXyxEeHo6oqKh6y6OiotC/f/9GX9OvX78G7bdu3YrevXvD1NT0hm3qtnkr70tEdCtsLeSYMdAP2+cOwU8zIzAuzA0mUgliUwrx399OIGLhdrz911lczC3Rd6lEHZJao8XCf+Lw3M+xKK/WYFBnR2x6ZmC7CXXALYzYTZw4EdOnT8cHH3yAO+64AxKJBIcOHcJ///tfTJo0CQBw6NAhBAYGtnStmDt3LqZMmYLevXujX79+WLVqFVJSUjBr1iwANYc/09PT8d133wGouQL2s88+w9y5czFz5kzs378fX3/9te5qV6DmnraDBw/GkiVLMHHiRPz555/Ytm0b9uzZ0+T3JSJqSRKJBP07OaJ/J0fkFFfgtyNp+OlgCtILy/H1niR8vScJ/fwd8Ehfb0SGukJuYlAzVxEZpILSKjz78zHsvZAPAJg9tBPmRQa1v4nHRTMVFxeLJ554QsjlciGVSoVUKhVyuVzMnDlTlJSUCCGEiI2NFbGxsc3ddJN8/vnnwsfHR8jlctGrVy8RExOjWzd16lQxZMiQeu2jo6NFz549hVwuF76+vmLFihUNtvnbb7+JoKAgYWpqKoKDg8W6deua9b5NUVRUJACIoqKiZr2OiEgIIdQardgRly2mrz4kfF/+S/i8VPMIf3urWPRPnLiUV6LvEomM1qm0QtF/0Xbh89JfIuS1zeLvkxlt+v7NyRC3PI9dSUkJEhMTIYRAp06dYGXF+4/eiL7uFUtExiftchnWHk7F2sOpyCm+Mq3SoM6OeLiPN+4MdYGpjKN4RC1h/bE0zF9/CpVqLfwcLbFySjgCXdr2IgneK7YdYrAjopZWrdFie1wOfjqUgt3nc1H329zJWoEHenviwTu84WVvod8iiQxUde35dKv3XgIADA92xkeTe0BpbtrmtbRqsCstLcXixYuxfft25OTkQKvV1lufmJjY/Io7AAY7ImpNqQVl+PlQCn49koa8kppRPIkEGNzZCQ9HeGNEsDNMOIpH1CR5JZV4+sdjOJhUAAB4bkRnzBnRGVI9nU/XqsHuoYceQkxMDKZMmQI3N7cGc6Y9//zzza+4A2CwI6K2UK3RIupsNn46mII9F/J0y11sFHigtxce6O3FUTyiG4g5l4uXfj+JLFUFrBQm+PCB7ojs4qrXmlo12Nna2uLvv//GgAEDbqvIjobBjoja2qW8Uvx8OAW/H0lDfmnNFFQSCTAwwBGT7/DCyFAXKEw4Lx4RAJRUqvHu32fx86GaGwp0crLEyim9EeCs/2sIWjXY+fn54Z9//kFISMhtFdnRMNgRkb5UqbXYejYLaw+n6m59BAD2lnLc09MDD/bxQoCz/mfMJ9KXfRfy8L/fTyK9sBwAMK2/L14aHQxzefv44NOqwe6HH37An3/+iW+//RYWFhzObyoGOyJqD1ILyvDrkVT8eiQV2aorV9T29rHD5Du8MC7MDRZy3qOWOobSSjWWbInHd/uTAQBe9uZ4777u6OvvoOfK6mvVYNezZ09cvHgRQgj4+vrq7uBQ59ixY82vuANgsCOi9kSt0SLmXC5+OZyKHfE50Ghr/hRYK0wwoYc7HrzDG908lXqukqj1HEoqwH9/O4GUgjIAwKN9vTF/TAgsFe3vg01zMkSzq6+7uwQRERkuE5kUI0JcMCLEBdmqCvx+NA1rD6cipaBMd4/aEDcb3BfuiUk93OFg1Tb3viZqbeVVGrz3bwJW70uCEICHrTmW3BuGgZ0d9V1ai+A8dm2EI3ZE1N5ptQIHEvPx8+FU/Hs6C1WamumsTKQSDA92xn3hnhgW7MzJj8lgHU2+jP/9dgKJeaUAgAfv8MKr40Jgbdb2c9M1BycobocY7IjIkBSWVWHTiQz8djQNJ9OKdMsdLOWY1NMD9/f2RLArf5eRYaio1uCjbefw5a5EaEXN9D+L7w3DsCBnfZfWJC0e7Ozt7XHu3Dk4OjrCzs6uwdx1VysoKGh+xR0Agx0RGaqErGL8fjQVG2LTkVdSpVve1cMG94d7YUJ3d9hZyvVYIVHjhBCITsjFO3+fxcXcmlG6e3p54I3xXaC0aN+jdFdr8WD37bff4sEHH4RCocC33357w7ZTp05tXrUdBIMdERm6ao0WMQm5+P1oGrbHZ6NaU/PnQy6T4s5QZ9zd0xNDAp0gN+GhWtK/sxkqLPwnTjdRt6OVAovu6YaRoS56rqz5Wu1QrFqtxo8//ohRo0bB1bVtZ2G+fPkynnvuOWzcuBEAMGHCBHz66aewtbW97muEEFiwYAFWrVqFy5cvIyIiAp9//jm6dOkCoGZ08Y033sDWrVuRmpoKR0dHTJo0CW+//TaUyitXg/n6+iI5Obnetl966SUsXry4yfUz2BGRMSkorcKfx9Px25E0nM1U6ZbbWphibDc3TOrhgd4+dnq7BRN1XFlFFfhgawJ+P5YGIWo+eEwb4IunhwXo5T6vLaFVz7GzsLBAXFwcfHx8bqvI5hozZgzS0tKwatUqAMB//vMf+Pr6YtOmTdd9zZIlS/Duu+9izZo1CAwMxDvvvINdu3YhISEB1tbWOH36NN544w1MmzYNoaGhSE5OxqxZsxAWFobff/9dtx1fX1/MmDEDM2fO1C2zsrKClVXTZ6NmsCMiY3Umowjrj6Vj04kM5BRfmRvPw9YcE3u4Y1JPDwS6cAJkal2llWqs3JWIL3clorxaAwAYH+aGl0YHG/xt9Fo12A0bNgzPP/98m057EhcXh9DQUBw4cAAREREAgAMHDqBfv36Ij49HUFBQg9cIIeDu7o45c+bgpZdeAgBUVlbCxcUFS5YswZNPPtnoe/3222949NFHUVpaChOTmtlgfH19MWfOHMyZM+eW94HBjoiMnUYrsP9iPv44no4tp7NQUqnWrQtxs8HdPd0xobsHXJVmeqySjI1GK/DbkVR8EHUOubUfLMJ97PDquBD08rbTc3Uto1XnsZs9ezbmzZuHtLQ0hIeHw9LSst76sLCw5m7ypvbv3w+lUqkLdQDQt29fKJVK7Nu3r9Fgl5SUhKysLERGRuqWKRQKDBkyBPv27btusKv7odWFujpLlizB22+/DS8vL9x///343//+B7n8+icLV1ZWorLyyidXlUp13bZERMZAJpVgYGdHDOzsiHcmdcX2uBxsiE1HzLkcxGWqEJepwqLN8ejr54BJPd0xqosrbC140QXduphzuVj4dxwSsosBAD4OFnh5dDBGd3W94YWexqzZwW7y5MkAgOeee063TCKRQAgBiUQCjUbTctXVysrKgrNzw0uSnZ2dkZWVdd3XAICLS/2TJF1cXBqcL1cnPz8fb7/9doPQ9/zzz6NXr16ws7PDoUOHMH/+fCQlJeGrr766bs2LFi3CggULbrhfRETGysxUhnFhbhgX5obCsir8fSoTf8Zm4NClAuxPzMf+xHy8uuE0+gc4Ylw3V4wMdYU9r6ylJqr7kLDrXC4AQGluiudGdMaUvj4d/uKdZge7pKSkFnvzN99886bh5/DhwwDQaPKuC5M3cu36671GpVJh3LhxCA0NxRtvvFFv3QsvvKD7PiwsDHZ2drjvvvuwZMkSODg0fj+5+fPnY+7cufW27+XldcNaiYiMka2FHI9E+OCRCB+kXS7DxhMZ2Hg8A/FZxdh1Lhe7zuXilQ2n0c/fAWO6uWJUF1c48k4XdA0hBPZdzMdXuxOxM6Em0JnKJHisny+eHR7A0d9azQ52LXnRxDPPPIMHH3zwhm18fX1x8uRJZGdnN1iXm5vbYESuTt1Vu1lZWXBzc9Mtz8nJafCa4uJijB49GlZWVtiwYUOD+99eq2/fvgCACxcuXDfYKRQKKBT8xUREdDVPOwvMHhqA2UMDkJhbgs2ns7D5dCZOp6uw50Ie9lzIw2t/nEYfP3uM7eaG0V1c4WzDc/I6siq1FptOZOCrPUmIq70CWyIBxnZ1w4ujg+DjYHmTLXQst3Sn2++//x5ffPEFkpKSsH//fvj4+GDZsmXw8/PDxIkTm7wdR0dHODre/N5s/fr1Q1FREQ4dOoQ+ffoAAA4ePIiioiL079+/0df4+fnB1dUVUVFR6NmzJwCgqqoKMTExWLJkia6dSqXCqFGjoFAosHHjRpiZ3fwXSGxsLADUC4xERNQ8/k5WeHpYAJ4eFoDk/NKakHcqEyfSinAgsQAHEgvwxsYzuMPHHmO6ueLOEBeDv7qRmq6wrAo/HkzBt/su6a62NjeV4YHennh8gB98HRnoGtPsq2JXrFiB119/HXPmzMG7776L06dPw9/fH2vWrMG3336LnTt3tkqhY8aMQUZGBlauXAmgZroTHx+fetOdBAcHY9GiRbj77rsB1FzwsGjRIqxevRqdO3fGwoULER0drZvupLi4GCNHjkRZWRk2bNhQ70IQJycnyGQy7N+/HwcOHMCwYcOgVCpx+PBhvPDCC+jduzf+/PPPJtfPq2KJiJomtaAM/57Jwt+nMhGbUlhvXaCLFYYFO2NEsAt6edvChPetNTpJeaX4Zk8Sfj+appu2xMVGgan9ffFwH+8Oeci1Vac7CQ0NxcKFCzFp0iRYW1vjxIkT8Pf3x+nTpzF06FDk5eXdVvHXU1BQ0GCC4s8++6zeBMUSiQSrV6/GtGnTAFyZoHjlypX1Jiju2rUrACA6OhrDhg1r9P2SkpLg6+uLY8eOYfbs2YiPj0dlZSV8fHzw4IMP4sUXX4SFRdM/OTLYERE1X0ZhObaczsKWM1k4mnwZGu2VP1lKc1MMCXTC8GBnDAl04m3NDJgQAgeTCvDV7iRsj89GXTIJdbPBzMF+GNfNvUNfFNGqwc7c3Bzx8fHw8fGpF+zOnz+PsLAwlJeX31bxxorBjojo9hSVVSPmfC52xGUj+lwuCsuqdeukEqCXt13NaF6IM4JcrDvsdBeGJL2wHH+fzMAfsRn17mAyItgZMwb5oZ+/A/sRrTyPnZ+fH44fP97gIorNmzcjNDS0uZsjIiJqEqWFKSZ0d8eE7u7QaAViUy5jR3wOdsTnID6rGEeSL+NI8mW8928CPGzNMSDAAf06OaCfvyMnRW5HclQV+PtUJv46mYmjyZd1yxUmUtwb7okZA/3Qyanpd3ai+pod7P73v//h6aefRkVFBYQQOHToEH7++WcsWrTohvO6ERERtRSZVILevvbo7WuPF0cHI72wHDvic7AzPgd7L+QhvbAcvx5Jw69H0gAAfo6W6OtfF/Qc4GTNWQvaUn5JJTafzsJfJzNwMKlAd6hVIgH6+NpjfHd3jOvmxrkMW0CzD8UCwJdffol33nkHqampAAAPDw+8+eabmDFjRosXaCx4KJaIqG2UV2lwICkf+y/WPM5kFEF7zV+6zs5WupAX4e/AQNEKisqq8e/ZLGw6kYF9F/PrnR/Zy9sW48PcMS7MDS6czuamWvUcu6vl5eVBq9U2elcIqo/BjohIP4rKq3EoqaAm6CXm6+ZCu1qwqzV6+dihu6cS3TxsEehixStum6lao8Xp9KKan3ViPvZeyEO15krE6Ophg7tqw5ynHaetaY5WD3ZqtRrR0dG4ePEiHn74YVhbWyMjIwM2NjawsuJx8cYw2BH9f3v3HtPk2f4B/NtSSrEtTAE5vDAL4otnx2EOjIc5nDoW46bJ9i7GYIxmGpx00zh1UZMlGyPZQaYT43Qu/rGwZKhZsoOQiWXqnANBmGzKTxDQ1SEoCKiVtvfvD6QTrdqytvA8fj/JE+vz3Le9Lq9ILu/nRDQ4XOu6jV97V/TqWnHu7877xmj8lRgXFYyJ0b3bE4gN0UKp5IX8vW5123C6qQ0n66/i5IWrKG+4hhu3+75WNCFcj3mTIvHixCjE8rlz/ebVxq6hoQFz585FY2MjLBYLzp07h7i4OBiNRty6dQs7d+78V8HLFRs7IqLBqaXTgpP1V3H6Yhuqmtrx+6V2dFis943Ta1SY8J9gTIgOxqTonlW9J4dpH5vHcHRarDjVcK2nkau/isqmNty22fuMCQ70x9OGYXgmdhhmJIThv+H6AYpWXrx6V2x2djZSUlJw+vTpPq/Tevnll7Fs2TL3oyUiIhpAoboAZEyIRMaEnrcJ2e0C9a1dqLrYhtNN7ai62IYzf11Hxy0rjp9vxfHzrY65SgUQM2wI4kK1iA3VITZMi5GhWsSGaRERpJHkozo6LVZcaOnC+SudqG/pQn1LF/6vuRN/Xu7oc50cAITpAzA5tqeRmxw7DP8drueq5gBzu7E7evQojh07BrW674WmI0aMwKVLlzwWGBER0UBQKhUYGabDyDAdXk6MBgBYbXac+7sTVRfbUHWpZ1XvfHMnum7b0NB6Aw2tNxwvpu8V6O+H2DtNXlyoFuFBGoTq1AjRBSBEq0aoPgD6ANWANH/dNjuart5wNG7nr3ShvqUTdVe6HK/vciZ6aOBdjVwIDCFDJNm8ypnbjZ3dbofNZrtv/8WLF6HXc8mViIjkR+WnxNioIIyNCsL/7uwTQuBKh+VOU/RPY1Tf0oXGqzdws9uGGvP1Pg/evZfaT4kQnbpn0wYgRKdGqC4Aw7RqaFRK+PkpoVIq4KdUOH7957Oyz74uixXXb1lx/WY32m924/qtbly/ab3r853tlhWdTk413y1Eq0ZcmLanMQ3VITZUiwnRwfjPE4Ee/Fslb3C7sXv++eexdetW7Nq1C0DPa7w6OzuxZcsWZGRkeDxAIiKiwUihUGB4kAbDgzRIGxnS59jdK2J1V7pQ39qFKx0WtHZa0Np1G62dt9FpseK2zQ5z+y2Y22/5PH6NvxKxoTrE3VlRjA3VIi5Mh9gQLYKH+Ps8HvIMt2+e+OuvvzBz5kz4+fmhtrYWKSkpqK2tRWhoKEpLS/nokwfgzRNERHS3W922O02eBa2dt9HiaPp6fm+x2WGzCVjtAja7HTYB2Ox2WG0CNnvv/n+OD1GrEBTojyCNCsGB/nc++9/5rLrrc8+YoUPUvB5OIrz+uJObN2+ioKAA5eXlsNvtSEpKwqJFixAYyCXaB2FjR0RERP3h1cautLQUU6ZMgUrV9yyu1WrF8ePHMX36dPcjfgywsSMiIqL+8OrjTmbOnAmz2XzfKdf29nbMnDnT6Y0V1HORLdBTHCIiIiJX9fYOrqzFud3YCSGc3trc2toKrZZPlX6Qjo4OAEBMTMwAR0JERERS1NHRgeDg4IeOcbmxW7BgAYCeu4CWLFmCgIAAxzGbzYaqqipMmTKln6HKX1RUFJqamqDX673yzJ/r168jJiYGTU1Nj8WpXuYrb8xX/h63nJmvvHk7XyEEOjo6EBUV9cixLjd2vR2iEAJ6vb7PjRJqtRqpqalYvnx5P8J9PCiVSkRHR3v9e4KCgh6Lf0S9mK+8MV/5e9xyZr7y5s18H7VS18vlxm7v3r0AAIPBgLVr1/K0KxEREdEg4/abi9etW9fnVGJDQwO2bt2KoqIijwZGRERERO5xu7GbP38+9u3bBwBoa2vD5MmT8dFHH2H+/PnIz8/3eIDkmoCAAGzZsqXPtY9yxnzljfnK3+OWM/OVt8GUr9vPsQsNDYXJZMK4ceOwe/dubNu2DRUVFSgsLMTmzZvxxx9/eCtWIiIiInoIt1fsbty4Ab1eDwAoKirCggULoFQqkZqaioaGBo8HSERERESucbuxi4+Px8GDB9HU1IRDhw5h9uzZAIDm5ubH6s4XIiIiosHG7cZu8+bNWLt2LQwGA5555hmkpaUB6Fm9S0xM9HiAREREROQat6+xA4DLly/DbDZj0qRJUCp7esOTJ08iKCgIo0eP9niQRERERPRobq/YAUBERAQSExMdTR0ATJ48mU2dl+3YsQOxsbHQaDRITk7Gzz///NDxJpMJycnJ0Gg0iIuLw86dO30UqWe4k++RI0egUCju2/78808fRtx/paWlmDdvHqKioqBQKHDw4MFHzpFyfd3NV8r1zcnJwdNPPw29Xo/hw4fjpZdewtmzZx85T6r17U++Uq4vAOTn52PixImOh9OmpaXhhx9+eOgcqdYXcD9fqdf3Xjk5OVAoFDAajQ8dN1A17ldjR7739ddfw2g04p133kFFRQWmTZuGF154AY2NjU7H19fXIyMjA9OmTUNFRQU2btyI1atXo7Cw0MeR94+7+fY6e/YszGazYxs1apSPIv53urq6MGnSJGzfvt2l8VKvr7v59pJifU0mE7KysnDixAkUFxfDarVi9uzZ6OrqeuAcKde3P/n2kmJ9ASA6OhoffPABysrKUFZWhueeew7z58/HmTNnnI6Xcn0B9/PtJdX63u23337Drl27MHHixIeOG9AaC5KEyZMnixUrVvTZN3r0aLF+/Xqn49etWydGjx7dZ9/rr78uUlNTvRajJ7mbb0lJiQAgrl275oPovAuAOHDgwEPHSL2+d3MlXznVt7m5WQAQJpPpgWPkVF9X8pVTfXsNHTpU7N692+kxOdW318PylUt9Ozo6xKhRo0RxcbGYMWOGyM7OfuDYgawxV+wk4Pbt2ygvL3fcgdxr9uzZOH78uNM5v/zyy33j58yZg7KyMnR3d3stVk/oT769EhMTERkZifT0dJSUlHgzzAEl5fr+G3Kob3t7OwBg2LBhDxwjp/q6km8vOdTXZrOhoKAAXV1djpsL7yWn+rqSby+p1zcrKwsvvvgiZs2a9cixA1ljNnYS0NLSApvNhvDw8D77w8PDcfnyZadzLl++7HS81WpFS0uL12L1hP7kGxkZiV27dqGwsBD79+9HQkIC0tPTUVpa6ouQfU7K9e0PudRXCIG33noLU6dOxfjx4x84Ti71dTVfOdS3uroaOp0OAQEBWLFiBQ4cOICxY8c6HSuH+rqTrxzqW1BQgFOnTiEnJ8el8QNZY5VX/3TyqLvf0Qv0/NC8d9+jxjvbP1i5k29CQgISEhIcv09LS0NTUxM+/PBDTJ8+3atxDhSp19cdcqnvqlWrUFVVhaNHjz5yrBzq62q+cqhvQkICKisr0dbWhsLCQmRmZsJkMj2w2ZF6fd3JV+r1bWpqQnZ2NoqKiqDRaFyeN1A15oqdBISGhsLPz+++1arm5ub7/kfQKyIiwul4lUqFkJAQr8XqCf3J15nU1FTU1tZ6OrxBQcr19RSp1feNN97At99+i5KSEkRHRz90rBzq606+zkitvmq1GvHx8UhJSUFOTg4mTZqEvLw8p2PlUF938nVGSvUtLy9Hc3MzkpOToVKpoFKpYDKZ8Omnn0KlUsFms903ZyBrzMZOAtRqNZKTk1FcXNxnf3FxMaZMmeJ0Tlpa2n3ji4qKkJKSAn9/f6/F6gn9ydeZiooKREZGejq8QUHK9fUUqdRXCIFVq1Zh//79OHz4MGJjYx85R8r17U++zkilvg8ihIDFYnF6TMr1fZCH5euMlOqbnp6O6upqVFZWOraUlBQsWrQIlZWV8PPzu2/OgNbY67dnkEcUFBQIf39/sWfPHlFTUyOMRqPQarXiwoULQggh1q9fLxYvXuwYX1dXJ4YMGSLefPNNUVNTI/bs2SP8/f3FN998M1ApuMXdfD/55BNx4MABce7cOfH777+L9evXCwCisLBwoFJwS0dHh6ioqBAVFRUCgPj4449FRUWFaGhoEELIr77u5ivl+q5cuVIEBweLI0eOCLPZ7Nhu3LjhGCOn+vYnXynXVwghNmzYIEpLS0V9fb2oqqoSGzduFEqlUhQVFQkh5FVfIdzPV+r1debeu2IHU43Z2EnIZ599JkaMGCHUarVISkrq8/iAzMxMMWPGjD7jjxw5IhITE4VarRYGg0Hk5+f7OOJ/x518c3NzxciRI4VGoxFDhw4VU6dOFd99990ARN0/vY8DuHfLzMwUQsivvu7mK+X6OssTgNi7d69jjJzq2598pVxfIYRYunSp42dVWFiYSE9PdzQ5QsirvkK4n6/U6+vMvY3dYKpxv14pRkRERESDD6+xIyIiIpIJNnZEREREMsHGjoiIiEgm2NgRERERyQQbOyIiIiKZYGNHREREJBNs7IiIiIhkgo0dERERkUywsSMi8hKDwQCFQgGFQoG2tjaffGfv9z3xxBM++T4iGlzY2BERuenZZ5+F0Wh0aey7774Ls9mM4OBg7wZ1h9lsxtatW33yXUQ0+KgGOgAiIjnT6/WIiIjw2fdFRET4rIkkosGHK3ZERG5YsmQJTCYT8vLyHKc9L1y44PL8hoYGzJs3D0OHDoVWq8W4cePw/fffO47X1NQgIyMDOp0O4eHhWLx4MVpaWhzH7XY7cnNzER8fj4CAADz55JN47733PJkiEUkYGzsiIjfk5eUhLS0Ny5cvh9lshtlsRkxMjMvzs7KyYLFYUFpaiurqauTm5kKn0wHoOY06Y8YMPPXUUygrK8OPP/6Iv//+G6+88opj/oYNG5Cbm4tNmzahpqYGX331FcLDwz2eJxFJE0/FEhG5ITg4GGq1GkOGDOnXKdbGxkYsXLgQEyZMAADExcU5juXn5yMpKQnvv/++Y98XX3yBmJgYnDt3DpGRkcjLy8P27duRmZkJABg5ciSmTp36L7MiIrlgY0dE5EOrV6/GypUrUVRUhFmzZmHhwoWYOHEiAKC8vBwlJSWOFby7nT9/Hm1tbbBYLEhPT/d12EQkETwVS0TkQ8uWLUNdXR0WL16M6upqpKSkYNu2bQB6rp+bN28eKisr+2y1tbWYPn06AgMDBzh6Ihrs2NgREblJrVbDZrP1e35MTAxWrFiB/fv3Y82aNfj8888BAElJSThz5gwMBgPi4+P7bFqtFqNGjUJgYCB++uknT6VCRDLDxo6IyE0GgwG//vorLly4gJaWFtjtdpfnGo1GHDp0CPX19Th16hQOHz6MMWPGAOi5seLq1at47bXXcPLkSdTV1aGoqAhLly6FzWaDRqPB22+/jXXr1mHfvn04f/48Tpw4gT179ngrVSKSGDZ2RERuWrt2Lfz8/DB27FiEhYWhsbHR5bk2mw1ZWVkYM2YM5s6di4SEBOzYsQMAEBUVhWPHjsFms2HOnDkYP348srOzERwcDKWy58f1pk2bsGbNGmzevBljxozBq6++iubmZq/kSUTSoxBCiIEOgohIjgwGA4xGo8tvqfCUL7/8Ekaj0WevMSOiwYONHRGRlxgMBpjNZvj7++PSpUs+eSOETqeD1WqFRqNhY0f0GOLjToiIvMRkMqG7uxtAz6vFfKGyshIA4Ofn55PvI6LBhSt2RERERDLBmyeIiIiIZIKNHREREZFMsLEjIiIikgk2dkREREQywcaOiIiISCbY2BERERHJBBs7IiIiIplgY0dEREQkE/8P1N0dgM8YGeoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a trajectory for the vehicle\n",
    "# Define the endpoints of the trajectory\n",
    "x0 = [0., -2., 0.]; u0 = [10., 0.]\n",
    "xf = [40., 2., 0.]; uf = [10., 0.]\n",
    "Tf = 4\n",
    "\n",
    "# Find a trajectory between the initial condition and the final condition\n",
    "traj = fs.point_to_point(vehicle, Tf, x0, u0, xf, uf, basis=fs.PolyFamily(6))\n",
    "\n",
    "# Create the desired trajectory between the initial and final condition\n",
    "Ts = 0.1\n",
    "timepts = np.arange(0, Tf + Ts, Ts)\n",
    "xd, ud = traj.eval(timepts)\n",
    "\n",
    "plot_lanechange(timepts, xd, ud)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeeaa39e",
   "metadata": {},
   "source": [
    "### Discrete time system model\n",
    "\n",
    "For the model that we use for the Kalman filter, we take a simple discretization using the approximation that $\\dot x = (x[k+1] - x[k])/T_s$ where $T_s$ is the sampling time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2469c60e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<StateSpace>: sys[0]$sampled\n",
      "Inputs (2): ['u[0]', 'u[1]']\n",
      "Outputs (3): ['y[0]', 'y[1]', 'y[2]']\n",
      "States (3): ['x[0]', 'x[1]', 'x[2]']\n",
      "dt = 0.1\n",
      "\n",
      "A = [[ 1.0000000e+00  0.0000000e+00 -5.0004445e-07]\n",
      "     [ 0.0000000e+00  1.0000000e+00  1.0000000e+00]\n",
      "     [ 0.0000000e+00  0.0000000e+00  1.0000000e+00]]\n",
      "\n",
      "B = [[ 9.99999999e-02 -8.33407417e-08]\n",
      "     [ 0.00000000e+00  1.66666667e-01]\n",
      "     [ 0.00000000e+00  3.33333333e-01]]\n",
      "\n",
      "C = [[1. 0. 0.]\n",
      "     [0. 1. 0.]\n",
      "     [0. 0. 1.]]\n",
      "\n",
      "D = [[0. 0.]\n",
      "     [0. 0.]\n",
      "     [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "#\n",
    "# Create a discrete-time, linear model\n",
    "#\n",
    "\n",
    "# Linearize about the starting point\n",
    "veh_lin = ct.linearize(vehicle, x0, u0)\n",
    "\n",
    "# Create a discrete-time model by hand\n",
    "veh_lin_dt = ct.sample_system(veh_lin, Ts)\n",
    "\n",
    "# Update the model to have full-state output\n",
    "# veh_lin_dt = ct.ss(\n",
    "#     veh_lin_dt.A, veh_lin_dt.B, np.eye(veh_lin_dt.nstates), 0, dt=veh_lin_dt.dt,\n",
    "#     name=\"vehicle-lin-dt\")\n",
    "print(veh_lin_dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "084c5ae8",
   "metadata": {},
   "source": [
    "### Sensor model\n",
    "\n",
    "We assume that we have two sensors: one with good longitudinal accuracy and the other with good lateral accuracy.  For each sensor we define the map from the state space to the sensor outputs, the covariance matrix for the measurements, and a white noise signal (now in discrete time)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0a19d109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sensor #1: longitudinal\n",
    "C_lon = np.eye(2, veh_lin_dt.nstates)\n",
    "Rw_lon = np.diag([0.1 ** 2, 1 ** 2])\n",
    "W_lon = ct.white_noise(timepts, Rw_lon, dt=Ts)\n",
    "\n",
    "# Sensor #2: lateral\n",
    "C_lat = np.eye(2, veh_lin_dt.nstates)\n",
    "Rw_lat = np.diag([1 ** 2, 0.1 ** 2])\n",
    "W_lat = ct.white_noise(timepts, Rw_lat, dt=Ts)\n",
    "\n",
    "# Plot the noisy signals\n",
    "plt.subplot(2, 1, 1)\n",
    "Y = xd[0:2] + W_lon\n",
    "plt.plot(Y[0], Y[1], label=\"measured\")\n",
    "plt.plot(xd[0], xd[1], **xdstyle, label=\"actual\")\n",
    "plt.xlabel(\"$x$ position [m]\")\n",
    "plt.ylabel(\"$y$ position [m]\")\n",
    "plt.title(\"Sensor #1\")\n",
    "plt.legend()\n",
    "               \n",
    "plt.subplot(2, 1, 2)\n",
    "Y = xd[0:2] + W_lat\n",
    "plt.plot(Y[0], Y[1])\n",
    "plt.plot(xd[0], xd[1], **xdstyle)\n",
    "plt.xlabel(\"$x$ position [m]\")\n",
    "plt.ylabel(\"$y$ position [m]\")\n",
    "plt.title(\"Sensor #2\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3fa1a3d",
   "metadata": {},
   "source": [
    "## Linear Quadratic Estimator\n",
    "\n",
    "To estimate the position of the vehicle, we construct an optimal estimator (Kalman filter)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "993601a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<NonlinearIOSystem>: sys[2]\n",
      "Inputs (6): ['y[0]', 'y[1]', 'y[2]', 'y[3]', 'u[0]', 'u[1]']\n",
      "Outputs (3): ['xhat[0]', 'xhat[1]', 'xhat[2]']\n",
      "States (12): ['xhat[0]', 'xhat[1]', 'xhat[2]', 'P[0,0]', 'P[0,1]', 'P[0,2]', 'P[1,0]', 'P[1,1]', 'P[1,2]', 'P[2,0]', 'P[2,1]', 'P[2,2]']\n",
      "dt = 0.1\n",
      "\n",
      "Update: <function create_estimator_iosystem.<locals>._estim_update at 0x141142d40>\n",
      "Output: <function create_estimator_iosystem.<locals>._estim_output at 0x141142700>\n"
     ]
    }
   ],
   "source": [
    "#\n",
    "# Create an estimator for the system\n",
    "#\n",
    "\n",
    "# Disturbance and initial condition model\n",
    "Rv = np.diag([0.1, 0.01]) * Ts\n",
    "# Rv = np.diag([10, 0.1]) * Ts  # No input data\n",
    "P0 = np.diag([1, 1, 0.1])\n",
    "\n",
    "# Combine the sensors\n",
    "C = np.vstack([C_lon, C_lat])\n",
    "Rw = sp.linalg.block_diag(Rw_lon, Rw_lat)\n",
    "\n",
    "estim = ct.create_estimator_iosystem(veh_lin_dt, Rv, Rw, C=C, P0=P0)\n",
    "print(estim)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9e2e618",
   "metadata": {},
   "source": [
    "Finally, we estimate the position of the vehicle based on sensor measurements.  We assume that the input to the vehicle (velocity and steering angle) is available, though we can also explore what happens if that information is not available (see commented out code below).\n",
    "\n",
    "We also carry out a prediction of the position of the vehicle by turning off the correction term in the Kalman filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3d02ec33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the inputs to the estimator\n",
    "Y = np.vstack([xd[0:2] + W_lon, xd[0:2] + W_lat])\n",
    "U = np.vstack([Y, ud])      # add input to the Kalman filter\n",
    "# U = np.vstack([Y, ud * 0])  # with no input information\n",
    "X0 = np.hstack([xd[:, 0], P0.reshape(-1)])\n",
    "\n",
    "# Run the estimator on the trajectory\n",
    "estim_resp = ct.input_output_response(estim, timepts, U, X0)\n",
    "\n",
    "# Run a prediction to see what happens next\n",
    "timepts_predict = np.arange(timepts[-1], timepts[-1] + 4 + Ts, Ts)\n",
    "U_predict = np.outer(U[:, -1], np.ones_like(timepts_predict))\n",
    "predict_resp = ct.input_output_response(\n",
    "    estim, timepts_predict, U_predict, estim_resp.states[:, -1],\n",
    "    params={'correct': False})\n",
    "\n",
    "# Plot the estimated trajectory versus the actual trajectory\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.errorbar(\n",
    "    estim_resp.time, estim_resp.outputs[0], \n",
    "    estim_resp.states[estim.find_state('P[0,0]')], \n",
    "    fmt='b-', **ebarstyle, label=\"estimated\")\n",
    "plt.errorbar(\n",
    "    predict_resp.time, predict_resp.outputs[0], \n",
    "    predict_resp.states[estim.find_state('P[0,0]')],\n",
    "    fmt='r-', **ebarstyle, label=\"predicted\")\n",
    "plt.plot(timepts, xd[0], 'k--', label=\"actual\")\n",
    "plt.ylabel(\"$x$ position [m]\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.errorbar(\n",
    "    estim_resp.time, estim_resp.outputs[1], \n",
    "    estim_resp.states[estim.find_state('P[1,1]')], fmt='b-', **ebarstyle)\n",
    "plt.errorbar(\n",
    "    predict_resp.time, predict_resp.outputs[1], \n",
    "    predict_resp.states[estim.find_state('P[1,1]')], fmt='r-', **ebarstyle)\n",
    "# lims = plt.axis(); plt.axis([lims[0], lims[1], -5, 5])\n",
    "plt.plot(timepts, xd[1], 'k--');\n",
    "plt.ylabel(\"$y$ position [m]\")\n",
    "plt.xlabel(\"Time $t$ [sec]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f9e3d59",
   "metadata": {},
   "source": [
    "More insight can be obtained by focusing on the errors in prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "44f69f79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the estimated errors\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.errorbar(\n",
    "    estim_resp.time, estim_resp.outputs[0] - xd[0], \n",
    "    estim_resp.states[estim.find_state('P[0,0]')],\n",
    "    fmt='b-', **ebarstyle, label=\"estimated\")\n",
    "plt.errorbar(\n",
    "    predict_resp.time, predict_resp.outputs[0] - (xd[0] + xd[0, -1]), \n",
    "    predict_resp.states[estim.find_state('P[0,0]')],\n",
    "    fmt='r-', **ebarstyle, label=\"predicted\")\n",
    "lims = plt.axis(); plt.axis([lims[0], lims[1], -0.2, 0.2])\n",
    "# lims = plt.axis(); plt.axis([lims[0], lims[1], -2, 0.2])\n",
    "plt.ylabel(\"$x$ error [m]\")\n",
    "plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.errorbar(\n",
    "    estim_resp.time, estim_resp.outputs[1] - xd[1], \n",
    "    estim_resp.states[estim.find_state('P[1,1]')], fmt='b-', **ebarstyle)\n",
    "plt.errorbar(\n",
    "    predict_resp.time, predict_resp.outputs[1] - xd[1, -1], \n",
    "    predict_resp.states[estim.find_state('P[1,1]')], fmt='r-', **ebarstyle)\n",
    "lims = plt.axis(); plt.axis([lims[0], lims[1], -0.2, 0.2])\n",
    "plt.ylabel(\"$y$ error [m]\")\n",
    "plt.xlabel(\"Time $t$ [sec]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f6c1b6f",
   "metadata": {},
   "source": [
    "### Things to try\n",
    "\n",
    "To gain a bit more insight into sensor fusion, you can try the following:\n",
    "\n",
    "* Remove the input (and update P0)\n",
    "* Change the sampling rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f680b92",
   "metadata": {},
   "source": [
    "### Predictor-corrector form\n",
    "\n",
    "Instead of using `create_estimator_iosystem`, we can also compute out the estimate in a more manual fashion, done here using the predictor-corrector form:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fa488d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# System matrices\n",
    "A, B, F = veh_lin_dt.A, veh_lin_dt.B, veh_lin_dt.B\n",
    "\n",
    "# Create an array to store the results\n",
    "xhat = np.zeros((veh_lin_dt.nstates, timepts.size))\n",
    "P = np.zeros((veh_lin_dt.nstates, veh_lin_dt.nstates, timepts.size))\n",
    "\n",
    "# Update the estimates at each time\n",
    "for i, t in enumerate(timepts):\n",
    "    # Prediction step\n",
    "    if i == 0:\n",
    "        # Use the initial condition\n",
    "        xkkm1 = xd[:, 0]\n",
    "        Pkkm1 = P0\n",
    "    else:\n",
    "        xkkm1 = A @ xkk + B @ ud[:, i-1]\n",
    "        Pkkm1 = A @ Pkk @ A.T + F @ Rv @ F.T\n",
    "    \n",
    "    # Correction step\n",
    "    L = Pkkm1 @ C.T @ np.linalg.inv(Rw + C @ Pkkm1 @ C.T)\n",
    "    xkk = xkkm1 - L @ (C @ xkkm1 - Y[:, i])\n",
    "    Pkk = Pkkm1 - L @ C @ Pkkm1\n",
    "\n",
    "    # Save the state estimate and covariance for later plotting\n",
    "    xhat[:, i], P[:, :, i] = xkk, Pkk\n",
    "    # xhat[:, i], P[:, :, i] = xkkm1, Pkkm1  # For comparison to Kalman form\n",
    "    \n",
    "plt.subplot(2, 1, 1)\n",
    "plt.errorbar(timepts, xhat[0], P[0, 0], fmt='b-', **ebarstyle, label=\"estimated\")\n",
    "plt.plot(timepts, xd[0], 'k--', label=\"actual\")\n",
    "plt.ylabel(\"$x$ position [m]\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.errorbar(timepts, xhat[1], P[1, 1], fmt='b-', **ebarstyle)\n",
    "plt.plot(timepts, xd[1], 'k--')\n",
    "plt.ylabel(\"$x$ position [m]\")\n",
    "plt.xlabel(\"Time $t$ [sec]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9d5cb32",
   "metadata": {},
   "source": [
    "We can compare the results of the predictor-corrector form to the Kalman filter form used at the top of the notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4eda4729",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the estimated errors (and compare to Kalman form)\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.errorbar(timepts, xhat[0] - xd[0], P[0, 0], fmt='b-', **ebarstyle, label=\"predictor-corrector\")\n",
    "plt.plot(estim_resp.time, estim_resp.outputs[0] - xd[0], 'r--', label=\"Kalman filter\")\n",
    "lims = plt.axis(); plt.axis([lims[0], lims[1], -0.2, 0.2])\n",
    "plt.ylabel(\"$x$ error [m]\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.errorbar(timepts, xhat[1] - xd[1], P[1, 1], fmt='b-', **ebarstyle)\n",
    "plt.plot(estim_resp.time, estim_resp.outputs[1] - xd[1], 'r--')\n",
    "lims = plt.axis(); plt.axis([lims[0], lims[1], -0.2, 0.2])\n",
    "plt.ylabel(\"$y$ error [m]\")\n",
    "plt.xlabel(\"Time $t$ [sec]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f7e3e4d",
   "metadata": {},
   "source": [
    "Note that the estimates are not the same!  It turns out that to get the correspondence of the two formulations, we need to define $\\hat{x}_\\text{KF}(k) = \\hat{x}_\\text{PC}(k|k-1)$ (see commented out code above)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
